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2",[569,1113,1115,1136],{"className":1114,"ariaHidden":599},[598],[569,1116,1118,1122,1125,1129,1133],{"className":1117},[603],[569,1119],{"className":1120,"style":1121},[607],"height:0.8193em;vertical-align:-0.136em;",[569,1123,590],{"className":1124,"style":614},[612,613],[569,1126],{"className":1127,"style":1128},[690],"margin-right:0.2778em;",[569,1130,1104],{"className":1131},[1132],"mrel",[569,1134],{"className":1135,"style":1128},[690],[569,1137,1139,1143],{"className":1138},[603],[569,1140],{"className":1141,"style":1142},[607],"height:0.6444em;",[569,1144,1108],{"className":1145},[612],"):",[569,1148,1151],{"className":1149},[1150],"katex-display",[569,1152,1154,1255],{"className":1153},[572],[569,1155,1157],{"className":1156},[576],[578,1158,1160],{"xmlns":580,"display":1159},"block",[582,1161,1162,1252],{},[585,1163,1164,1167,1170,1172,1174,1177,1179,1182,1188,1191,1194,1197,1199,1201,1203,1205,1207,1209,1215,1232,1234],{},[588,1165,1166],{},"E",[666,1168,802],{"stretchy":1169},"false",[588,1171,758],{},[666,1173,813],{"stretchy":1169},[666,1175,1176],{},"=",[588,1178,723],{},[666,1180,1181],{},"⋅",[804,1183,1184,1186],{},[588,1185,630],{},[588,1187,590],{},[666,1189,1190],{"separator":599},",",[690,1192],{"width":1193},"2em",[588,1195,1196],{},"V",[666,1198,802],{"stretchy":1169},[588,1200,758],{},[666,1202,813],{"stretchy":1169},[666,1204,1176],{},[588,1206,723],{},[666,1208,1181],{},[804,1210,1211,1213],{},[588,1212,630],{},[588,1214,590],{},[585,1216,1217,1219,1222,1224,1230],{},[666,1218,802],{"fence":599},[1106,1220,1221],{},"1",[666,1223,668],{},[804,1225,1226,1228],{},[588,1227,630],{},[588,1229,590],{},[666,1231,813],{"fence":599},[666,1233,1181],{},[804,1235,1236,1244],{},[585,1237,1238,1240,1242],{},[588,1239,590],{},[666,1241,668],{},[588,1243,723],{},[585,1245,1246,1248,1250],{},[588,1247,590],{},[666,1249,668],{},[1106,1251,1221],{},[592,1253,1254],{"encoding":594},"E(X) = n \\cdot \\frac{M}{N}, \\qquad V(X) = n \\cdot \\frac{M}{N}\\left(1 - \\frac{M}{N}\\right) \\cdot \\frac{N-n}{N-1}",[569,1256,1258,1287,1306,1417,1435,1606],{"className":1257,"ariaHidden":599},[598],[569,1259,1261,1265,1269,1272,1275,1278,1281,1284],{"className":1260},[603],[569,1262],{"className":1263,"style":1264},[607],"height:1em;vertical-align:-0.25em;",[569,1266,1166],{"className":1267,"style":1268},[612,613],"margin-right:0.0576em;",[569,1270,802],{"className":1271},[833],[569,1273,758],{"className":1274,"style":773},[612,613],[569,1276,813],{"className":1277},[911],[569,1279],{"className":1280,"style":1128},[690],[569,1282,1176],{"className":1283},[1132],[569,1285],{"className":1286,"style":1128},[690],[569,1288,1290,1294,1297,1300,1303],{"className":1289},[603],[569,1291],{"className":1292,"style":1293},[607],"height:0.4445em;",[569,1295,723],{"className":1296},[612,613],[569,1298],{"className":1299,"style":691},[690],[569,1301,1181],{"className":1302},[695],[569,1304],{"className":1305,"style":691},[690],[569,1307,1309,1313,1384,1388,1392,1396,1399,1402,1405,1408,1411,1414],{"className":1308},[603],[569,1310],{"className":1311,"style":1312},[607],"height:2.0463em;vertical-align:-0.686em;",[569,1314,1316,1320,1381],{"className":1315},[612],[569,1317],{"className":1318},[833,1319],"nulldelimiter",[569,1321,1323],{"className":1322},[804],[569,1324,1326,1372],{"className":1325},[847,848],[569,1327,1329,1369],{"className":1328},[852],[569,1330,1333,1346,1357],{"className":1331,"style":1332},[856],"height:1.3603em;",[569,1334,1336,1340],{"style":1335},"top:-2.314em;",[569,1337],{"className":1338,"style":1339},[864],"height:3em;",[569,1341,1343],{"className":1342},[612],[569,1344,590],{"className":1345,"style":614},[612,613],[569,1347,1349,1352],{"style":1348},"top:-3.23em;",[569,1350],{"className":1351,"style":1339},[864],[569,1353],{"className":1354,"style":1356},[1355],"frac-line","border-bottom-width:0.04em;",[569,1358,1360,1363],{"style":1359},"top:-3.677em;",[569,1361],{"className":1362,"style":1339},[864],[569,1364,1366],{"className":1365},[612],[569,1367,630],{"className":1368,"style":614},[612,613],[569,1370,898],{"className":1371},[897],[569,1373,1375],{"className":1374},[852],[569,1376,1379],{"className":1377,"style":1378},[856],"height:0.686em;",[569,1380],{},[569,1382],{"className":1383},[911,1319],[569,1385,1190],{"className":1386},[1387],"mpunct",[569,1389],{"className":1390,"style":1391},[690],"margin-right:2em;",[569,1393],{"className":1394,"style":1395},[690],"margin-right:0.1667em;",[569,1397,1196],{"className":1398,"style":691},[612,613],[569,1400,802],{"className":1401},[833],[569,1403,758],{"className":1404,"style":773},[612,613],[569,1406,813],{"className":1407},[911],[569,1409],{"className":1410,"style":1128},[690],[569,1412,1176],{"className":1413},[1132],[569,1415],{"className":1416,"style":1128},[690],[569,1418,1420,1423,1426,1429,1432],{"className":1419},[603],[569,1421],{"className":1422,"style":1293},[607],[569,1424,723],{"className":1425},[612,613],[569,1427],{"className":1428,"style":691},[690],[569,1430,1181],{"className":1431},[695],[569,1433],{"className":1434,"style":691},[690],[569,1436,1438,1442,1504,1507,1597,1600,1603],{"className":1437},[603],[569,1439],{"className":1440,"style":1441},[607],"height:2.4em;vertical-align:-0.95em;",[569,1443,1445,1448,1501],{"className":1444},[612],[569,1446],{"className":1447},[833,1319],[569,1449,1451],{"className":1450},[804],[569,1452,1454,1493],{"className":1453},[847,848],[569,1455,1457,1490],{"className":1456},[852],[569,1458,1460,1471,1479],{"className":1459,"style":1332},[856],[569,1461,1462,1465],{"style":1335},[569,1463],{"className":1464,"style":1339},[864],[569,1466,1468],{"className":1467},[612],[569,1469,590],{"className":1470,"style":614},[612,613],[569,1472,1473,1476],{"style":1348},[569,1474],{"className":1475,"style":1339},[864],[569,1477],{"className":1478,"style":1356},[1355],[569,1480,1481,1484],{"style":1359},[569,1482],{"className":1483,"style":1339},[864],[569,1485,1487],{"className":1486},[612],[569,1488,630],{"className":1489,"style":614},[612,613],[569,1491,898],{"className":1492},[897],[569,1494,1496],{"className":1495},[852],[569,1497,1499],{"className":1498,"style":1378},[856],[569,1500],{},[569,1502],{"className":1503},[911,1319],[569,1505],{"className":1506,"style":1395},[690],[569,1508,1511,1517,1520,1523,1526,1529,1591],{"className":1509},[1510],"minner",[569,1512,1514],{"className":1513,"style":835},[833,834],[569,1515,802],{"className":1516},[839,871],[569,1518,1221],{"className":1519},[612],[569,1521],{"className":1522,"style":691},[690],[569,1524,668],{"className":1525},[695],[569,1527],{"className":1528,"style":691},[690],[569,1530,1532,1535,1588],{"className":1531},[612],[569,1533],{"className":1534},[833,1319],[569,1536,1538],{"className":1537},[804],[569,1539,1541,1580],{"className":1540},[847,848],[569,1542,1544,1577],{"className":1543},[852],[569,1545,1547,1558,1566],{"className":1546,"style":1332},[856],[569,1548,1549,1552],{"style":1335},[569,1550],{"className":1551,"style":1339},[864],[569,1553,1555],{"className":1554},[612],[569,1556,590],{"className":1557,"style":614},[612,613],[569,1559,1560,1563],{"style":1348},[569,1561],{"className":1562,"style":1339},[864],[569,1564],{"className":1565,"style":1356},[1355],[569,1567,1568,1571],{"style":1359},[569,1569],{"className":1570,"style":1339},[864],[569,1572,1574],{"className":1573},[612],[569,1575,630],{"className":1576,"style":614},[612,613],[569,1578,898],{"className":1579},[897],[569,1581,1583],{"className":1582},[852],[569,1584,1586],{"className":1585,"style":1378},[856],[569,1587],{},[569,1589],{"className":1590},[911,1319],[569,1592,1594],{"className":1593,"style":835},[911,834],[569,1595,813],{"className":1596},[839,871],[569,1598],{"className":1599,"style":691},[690],[569,1601,1181],{"className":1602},[695],[569,1604],{"className":1605,"style":691},[690],[569,1607,1609,1613],{"className":1608},[603],[569,1610],{"className":1611,"style":1612},[607],"height:2.1297em;vertical-align:-0.7693em;",[569,1614,1616,1619,1697],{"className":1615},[612],[569,1617],{"className":1618},[833,1319],[569,1620,1622],{"className":1621},[804],[569,1623,1625,1688],{"className":1624},[847,848],[569,1626,1628,1685],{"className":1627},[852],[569,1629,1631,1654,1662],{"className":1630,"style":1332},[856],[569,1632,1633,1636],{"style":1335},[569,1634],{"className":1635,"style":1339},[864],[569,1637,1639,1642,1645,1648,1651],{"className":1638},[612],[569,1640,590],{"className":1641,"style":614},[612,613],[569,1643],{"className":1644,"style":691},[690],[569,1646,668],{"className":1647},[695],[569,1649],{"className":1650,"style":691},[690],[569,1652,1221],{"className":1653},[612],[569,1655,1656,1659],{"style":1348},[569,1657],{"className":1658,"style":1339},[864],[569,1660],{"className":1661,"style":1356},[1355],[569,1663,1664,1667],{"style":1359},[569,1665],{"className":1666,"style":1339},[864],[569,1668,1670,1673,1676,1679,1682],{"className":1669},[612],[569,1671,590],{"className":1672,"style":614},[612,613],[569,1674],{"className":1675,"style":691},[690],[569,1677,668],{"className":1678},[695],[569,1680],{"className":1681,"style":691},[690],[569,1683,723],{"className":1684},[612,613],[569,1686,898],{"className":1687},[897],[569,1689,1691],{"className":1690},[852],[569,1692,1695],{"className":1693,"style":1694},[856],"height:0.7693em;",[569,1696],{},[569,1698],{"className":1699},[911,1319],[565,1701,1702,1703,1731,1732,1760,1761,1789,1790,1818,1819,1944],{},"Der letzte Faktor ist kleiner als ",[569,1704,1706,1719],{"className":1705},[572],[569,1707,1709],{"className":1708},[576],[578,1710,1711],{"xmlns":580},[582,1712,1713,1717],{},[585,1714,1715],{},[1106,1716,1221],{},[592,1718,1221],{"encoding":594},[569,1720,1722],{"className":1721,"ariaHidden":599},[598],[569,1723,1725,1728],{"className":1724},[603],[569,1726],{"className":1727,"style":1142},[607],[569,1729,1221],{"className":1730},[612],": Ohne Zurücklegen streut ",[569,1733,1735,1748],{"className":1734},[572],[569,1736,1738],{"className":1737},[576],[578,1739,1740],{"xmlns":580},[582,1741,1742,1746],{},[585,1743,1744],{},[588,1745,758],{},[592,1747,758],{"encoding":594},[569,1749,1751],{"className":1750,"ariaHidden":599},[598],[569,1752,1754,1757],{"className":1753},[603],[569,1755],{"className":1756,"style":608},[607],[569,1758,758],{"className":1759,"style":773},[612,613]," weniger als bei der Binomialverteilung. Ist ",[569,1762,1764,1777],{"className":1763},[572],[569,1765,1767],{"className":1766},[576],[578,1768,1769],{"xmlns":580},[582,1770,1771,1775],{},[585,1772,1773],{},[588,1774,590],{},[592,1776,590],{"encoding":594},[569,1778,1780],{"className":1779,"ariaHidden":599},[598],[569,1781,1783,1786],{"className":1782},[603],[569,1784],{"className":1785,"style":608},[607],[569,1787,590],{"className":1788,"style":614},[612,613]," sehr groß im Vergleich zu ",[569,1791,1793,1806],{"className":1792},[572],[569,1794,1796],{"className":1795},[576],[578,1797,1798],{"xmlns":580},[582,1799,1800,1804],{},[585,1801,1802],{},[588,1803,723],{},[592,1805,723],{"encoding":594},[569,1807,1809],{"className":1808,"ariaHidden":599},[598],[569,1810,1812,1815],{"className":1811},[603],[569,1813],{"className":1814,"style":735},[607],[569,1816,723],{"className":1817},[612,613],", ändert sich der Trefferanteil beim Ziehen kaum. Dann kann man näherungsweise mit der Binomialverteilung und ",[569,1820,1822,1844],{"className":1821},[572],[569,1823,1825],{"className":1824},[576],[578,1826,1827],{"xmlns":580},[582,1828,1829,1841],{},[585,1830,1831,1833,1835],{},[588,1832,565],{},[666,1834,1176],{},[804,1836,1837,1839],{},[588,1838,630],{},[588,1840,590],{},[592,1842,1843],{"encoding":594},"p = \\frac{M}{N}",[569,1845,1847,1866],{"className":1846,"ariaHidden":599},[598],[569,1848,1850,1854,1857,1860,1863],{"className":1849},[603],[569,1851],{"className":1852,"style":1853},[607],"height:0.625em;vertical-align:-0.1944em;",[569,1855,565],{"className":1856},[612,613],[569,1858],{"className":1859,"style":1128},[690],[569,1861,1176],{"className":1862},[1132],[569,1864],{"className":1865,"style":1128},[690],[569,1867,1869,1873],{"className":1868},[603],[569,1870],{"className":1871,"style":1872},[607],"height:1.2173em;vertical-align:-0.345em;",[569,1874,1876,1879,1941],{"className":1875},[612],[569,1877],{"className":1878},[833,1319],[569,1880,1882],{"className":1881},[804],[569,1883,1885,1933],{"className":1884},[847,848],[569,1886,1888,1930],{"className":1887},[852],[569,1889,1892,1907,1915],{"className":1890,"style":1891},[856],"height:0.8723em;",[569,1893,1895,1898],{"style":1894},"top:-2.655em;",[569,1896],{"className":1897,"style":1339},[864],[569,1899,1901],{"className":1900},[869,870,871,872],[569,1902,1904],{"className":1903},[612,872],[569,1905,590],{"className":1906,"style":614},[612,613,872],[569,1908,1909,1912],{"style":1348},[569,1910],{"className":1911,"style":1339},[864],[569,1913],{"className":1914,"style":1356},[1355],[569,1916,1918,1921],{"style":1917},"top:-3.394em;",[569,1919],{"className":1920,"style":1339},[864],[569,1922,1924],{"className":1923},[869,870,871,872],[569,1925,1927],{"className":1926},[612,872],[569,1928,630],{"className":1929,"style":614},[612,613,872],[569,1931,898],{"className":1932},[897],[569,1934,1936],{"className":1935},[852],[569,1937,1939],{"className":1938,"style":905},[856],[569,1940],{},[569,1942],{"className":1943},[911,1319]," rechnen.",[560,1946,1948],{"id":1947},"beispiele","Beispiele",[565,1950,1951,1952,615,1981,2010,2011,2040,2041,2069],{},"In einer Urne liegen ",[569,1953,1955,1969],{"className":1954},[572],[569,1956,1958],{"className":1957},[576],[578,1959,1960],{"xmlns":580},[582,1961,1962,1967],{},[585,1963,1964],{},[1106,1965,1966],{},"10",[592,1968,1966],{"encoding":594},[569,1970,1972],{"className":1971,"ariaHidden":599},[598],[569,1973,1975,1978],{"className":1974},[603],[569,1976],{"className":1977,"style":1142},[607],[569,1979,1966],{"className":1980},[612],[569,1982,1984,1998],{"className":1983},[572],[569,1985,1987],{"className":1986},[576],[578,1988,1989],{"xmlns":580},[582,1990,1991,1996],{},[585,1992,1993],{},[1106,1994,1995],{},"4",[592,1997,1995],{"encoding":594},[569,1999,2001],{"className":2000,"ariaHidden":599},[598],[569,2002,2004,2007],{"className":2003},[603],[569,2005],{"className":2006,"style":1142},[607],[569,2008,1995],{"className":2009},[612]," rot. Es werden ",[569,2012,2014,2028],{"className":2013},[572],[569,2015,2017],{"className":2016},[576],[578,2018,2019],{"xmlns":580},[582,2020,2021,2026],{},[585,2022,2023],{},[1106,2024,2025],{},"3",[592,2027,2025],{"encoding":594},[569,2029,2031],{"className":2030,"ariaHidden":599},[598],[569,2032,2034,2037],{"className":2033},[603],[569,2035],{"className":2036,"style":1142},[607],[569,2038,2025],{"className":2039},[612]," gezogen. Genau ",[569,2042,2044,2057],{"className":2043},[572],[569,2045,2047],{"className":2046},[576],[578,2048,2049],{"xmlns":580},[582,2050,2051,2055],{},[585,2052,2053],{},[1106,2054,1108],{},[592,2056,1108],{"encoding":594},[569,2058,2060],{"className":2059,"ariaHidden":599},[598],[569,2061,2063,2066],{"className":2062},[603],[569,2064],{"className":2065,"style":1142},[607],[569,2067,1108],{"className":2068},[612]," rote:",[569,2071,2073],{"className":2072},[1150],[569,2074,2076,2166],{"className":2075},[572],[569,2077,2079],{"className":2078},[576],[578,2080,2081],{"xmlns":580,"display":1159},[582,2082,2083,2163],{},[585,2084,2085,2088,2090,2092,2094,2096,2098,2100,2143,2145,2158,2160],{},[588,2086,2087],{},"P",[666,2089,802],{"stretchy":1169},[588,2091,758],{},[666,2093,1176],{},[1106,2095,1108],{},[666,2097,813],{"stretchy":1169},[666,2099,1176],{},[804,2101,2102,2131],{},[585,2103,2104,2116,2118],{},[585,2105,2106,2108,2114],{},[666,2107,802],{"fence":599},[804,2109,2110,2112],{"linethickness":806},[1106,2111,1995],{},[1106,2113,1108],{},[666,2115,813],{"fence":599},[666,2117,1181],{},[585,2119,2120,2122,2129],{},[666,2121,802],{"fence":599},[804,2123,2124,2127],{"linethickness":806},[1106,2125,2126],{},"6",[1106,2128,1221],{},[666,2130,813],{"fence":599},[585,2132,2133,2135,2141],{},[666,2134,802],{"fence":599},[804,2136,2137,2139],{"linethickness":806},[1106,2138,1966],{},[1106,2140,2025],{},[666,2142,813],{"fence":599},[666,2144,1176],{},[804,2146,2147,2155],{},[585,2148,2149,2151,2153],{},[1106,2150,2126],{},[666,2152,1181],{},[1106,2154,2126],{},[1106,2156,2157],{},"120",[666,2159,1176],{},[1106,2161,2162],{},"0,3",[592,2164,2165],{"encoding":594},"P(X = 2) = \\frac{\\binom{4}{2} \\cdot \\binom{6}{1}}{\\binom{10}{3}} = \\frac{6 \\cdot 6}{120} = 0{,}3",[569,2167,2169,2194,2215,2499,2590],{"className":2168,"ariaHidden":599},[598],[569,2170,2172,2175,2179,2182,2185,2188,2191],{"className":2171},[603],[569,2173],{"className":2174,"style":1264},[607],[569,2176,2087],{"className":2177,"style":2178},[612,613],"margin-right:0.1389em;",[569,2180,802],{"className":2181},[833],[569,2183,758],{"className":2184,"style":773},[612,613],[569,2186],{"className":2187,"style":1128},[690],[569,2189,1176],{"className":2190},[1132],[569,2192],{"className":2193,"style":1128},[690],[569,2195,2197,2200,2203,2206,2209,2212],{"className":2196},[603],[569,2198],{"className":2199,"style":1264},[607],[569,2201,1108],{"className":2202},[612],[569,2204,813],{"className":2205},[911],[569,2207],{"className":2208,"style":1128},[690],[569,2210,1176],{"className":2211},[1132],[569,2213],{"className":2214,"style":1128},[690],[569,2216,2218,2222,2490,2493,2496],{"className":2217},[603],[569,2219],{"className":2220,"style":2221},[607],"height:2.7702em;vertical-align:-1.1351em;",[569,2223,2225,2228,2487],{"className":2224},[612],[569,2226],{"className":2227},[833,1319],[569,2229,2231],{"className":2230},[804],[569,2232,2234,2478],{"className":2233},[847,848],[569,2235,2237,2475],{"className":2236},[852],[569,2238,2241,2317,2325],{"className":2239,"style":2240},[856],"height:1.6351em;",[569,2242,2244,2247],{"style":2243},"top:-2.2149em;",[569,2245],{"className":2246,"style":1339},[864],[569,2248,2250],{"className":2249},[612],[569,2251,2253,2259,2311],{"className":2252},[612],[569,2254,2256],{"className":2255,"style":835},[833,834],[569,2257,802],{"className":2258},[839,840],[569,2260,2262],{"className":2261},[804],[569,2263,2265,2303],{"className":2264},[847,848],[569,2266,2268,2300],{"className":2267},[852],[569,2269,2272,2286],{"className":2270,"style":2271},[856],"height:0.8951em;",[569,2273,2274,2277],{"style":860},[569,2275],{"className":2276,"style":865},[864],[569,2278,2280],{"className":2279},[869,870,871,872],[569,2281,2283],{"className":2282},[612,872],[569,2284,2025],{"className":2285},[612,872],[569,2287,2288,2291],{"style":881},[569,2289],{"className":2290,"style":865},[864],[569,2292,2294],{"className":2293},[869,870,871,872],[569,2295,2297],{"className":2296},[612,872],[569,2298,1966],{"className":2299},[612,872],[569,2301,898],{"className":2302},[897],[569,2304,2306],{"className":2305},[852],[569,2307,2309],{"className":2308,"style":905},[856],[569,2310],{},[569,2312,2314],{"className":2313,"style":835},[911,834],[569,2315,813],{"className":2316},[839,840],[569,2318,2319,2322],{"style":1348},[569,2320],{"className":2321,"style":1339},[864],[569,2323],{"className":2324,"style":1356},[1355],[569,2326,2328,2331],{"style":2327},"top:-3.74em;",[569,2329],{"className":2330,"style":1339},[864],[569,2332,2334,2400,2403,2406,2409],{"className":2333},[612],[569,2335,2337,2343,2394],{"className":2336},[612],[569,2338,2340],{"className":2339,"style":835},[833,834],[569,2341,802],{"className":2342},[839,840],[569,2344,2346],{"className":2345},[804],[569,2347,2349,2386],{"className":2348},[847,848],[569,2350,2352,2383],{"className":2351},[852],[569,2353,2355,2369],{"className":2354,"style":2271},[856],[569,2356,2357,2360],{"style":860},[569,2358],{"className":2359,"style":865},[864],[569,2361,2363],{"className":2362},[869,870,871,872],[569,2364,2366],{"className":2365},[612,872],[569,2367,1108],{"className":2368},[612,872],[569,2370,2371,2374],{"style":881},[569,2372],{"className":2373,"style":865},[864],[569,2375,2377],{"className":2376},[869,870,871,872],[569,2378,2380],{"className":2379},[612,872],[569,2381,1995],{"className":2382},[612,872],[569,2384,898],{"className":2385},[897],[569,2387,2389],{"className":2388},[852],[569,2390,2392],{"className":2391,"style":905},[856],[569,2393],{},[569,2395,2397],{"className":2396,"style":835},[911,834],[569,2398,813],{"className":2399},[839,840],[569,2401],{"className":2402,"style":691},[690],[569,2404,1181],{"className":2405},[695],[569,2407],{"className":2408,"style":691},[690],[569,2410,2412,2418,2469],{"className":2411},[612],[569,2413,2415],{"className":2414,"style":835},[833,834],[569,2416,802],{"className":2417},[839,840],[569,2419,2421],{"className":2420},[804],[569,2422,2424,2461],{"className":2423},[847,848],[569,2425,2427,2458],{"className":2426},[852],[569,2428,2430,2444],{"className":2429,"style":2271},[856],[569,2431,2432,2435],{"style":860},[569,2433],{"className":2434,"style":865},[864],[569,2436,2438],{"className":2437},[869,870,871,872],[569,2439,2441],{"className":2440},[612,872],[569,2442,1221],{"className":2443},[612,872],[569,2445,2446,2449],{"style":881},[569,2447],{"className":2448,"style":865},[864],[569,2450,2452],{"className":2451},[869,870,871,872],[569,2453,2455],{"className":2454},[612,872],[569,2456,2126],{"className":2457},[612,872],[569,2459,898],{"className":2460},[897],[569,2462,2464],{"className":2463},[852],[569,2465,2467],{"className":2466,"style":905},[856],[569,2468],{},[569,2470,2472],{"className":2471,"style":835},[911,834],[569,2473,813],{"className":2474},[839,840],[569,2476,898],{"className":2477},[897],[569,2479,2481],{"className":2480},[852],[569,2482,2485],{"className":2483,"style":2484},[856],"height:1.1351em;",[569,2486],{},[569,2488],{"className":2489},[911,1319],[569,2491],{"className":2492,"style":1128},[690],[569,2494,1176],{"className":2495},[1132],[569,2497],{"className":2498,"style":1128},[690],[569,2500,2502,2506,2581,2584,2587],{"className":2501},[603],[569,2503],{"className":2504,"style":2505},[607],"height:2.0074em;vertical-align:-0.686em;",[569,2507,2509,2512,2578],{"className":2508},[612],[569,2510],{"className":2511},[833,1319],[569,2513,2515],{"className":2514},[804],[569,2516,2518,2570],{"className":2517},[847,848],[569,2519,2521,2567],{"className":2520},[852],[569,2522,2525,2536,2544],{"className":2523,"style":2524},[856],"height:1.3214em;",[569,2526,2527,2530],{"style":1335},[569,2528],{"className":2529,"style":1339},[864],[569,2531,2533],{"className":2532},[612],[569,2534,2157],{"className":2535},[612],[569,2537,2538,2541],{"style":1348},[569,2539],{"className":2540,"style":1339},[864],[569,2542],{"className":2543,"style":1356},[1355],[569,2545,2546,2549],{"style":1359},[569,2547],{"className":2548,"style":1339},[864],[569,2550,2552,2555,2558,2561,2564],{"className":2551},[612],[569,2553,2126],{"className":2554},[612],[569,2556],{"className":2557,"style":691},[690],[569,2559,1181],{"className":2560},[695],[569,2562],{"className":2563,"style":691},[690],[569,2565,2126],{"className":2566},[612],[569,2568,898],{"className":2569},[897],[569,2571,2573],{"className":2572},[852],[569,2574,2576],{"className":2575,"style":1378},[856],[569,2577],{},[569,2579],{"className":2580},[911,1319],[569,2582],{"className":2583,"style":1128},[690],[569,2585,1176],{"className":2586},[1132],[569,2588],{"className":2589,"style":1128},[690],[569,2591,2593,2597,2601,2607],{"className":2592},[603],[569,2594],{"className":2595,"style":2596},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,2598,2600],{"className":2599},[612],"0",[569,2602,2604],{"className":2603},[612],[569,2605,1190],{"className":2606},[1387],[569,2608,2025],{"className":2609},[612],[565,2611,2612,2613,2804,2805,777],{},"Im Mittel zieht man ",[569,2614,2616,2653],{"className":2615},[572],[569,2617,2619],{"className":2618},[576],[578,2620,2621],{"xmlns":580},[582,2622,2623,2650],{},[585,2624,2625,2627,2629,2631,2633,2635,2637,2639,2645,2647],{},[588,2626,1166],{},[666,2628,802],{"stretchy":1169},[588,2630,758],{},[666,2632,813],{"stretchy":1169},[666,2634,1176],{},[1106,2636,2025],{},[666,2638,1181],{},[804,2640,2641,2643],{},[1106,2642,1995],{},[1106,2644,1966],{},[666,2646,1176],{},[1106,2648,2649],{},"1,2",[592,2651,2652],{"encoding":594},"E(X) = 3 \\cdot \\frac{4}{10} = 1{,}2",[569,2654,2656,2683,2701,2786],{"className":2655,"ariaHidden":599},[598],[569,2657,2659,2662,2665,2668,2671,2674,2677,2680],{"className":2658},[603],[569,2660],{"className":2661,"style":1264},[607],[569,2663,1166],{"className":2664,"style":1268},[612,613],[569,2666,802],{"className":2667},[833],[569,2669,758],{"className":2670,"style":773},[612,613],[569,2672,813],{"className":2673},[911],[569,2675],{"className":2676,"style":1128},[690],[569,2678,1176],{"className":2679},[1132],[569,2681],{"className":2682,"style":1128},[690],[569,2684,2686,2689,2692,2695,2698],{"className":2685},[603],[569,2687],{"className":2688,"style":1142},[607],[569,2690,2025],{"className":2691},[612],[569,2693],{"className":2694,"style":691},[690],[569,2696,1181],{"className":2697},[695],[569,2699],{"className":2700,"style":691},[690],[569,2702,2704,2708,2777,2780,2783],{"className":2703},[603],[569,2705],{"className":2706,"style":2707},[607],"height:1.1901em;vertical-align:-0.345em;",[569,2709,2711,2714,2774],{"className":2710},[612],[569,2712],{"className":2713},[833,1319],[569,2715,2717],{"className":2716},[804],[569,2718,2720,2766],{"className":2719},[847,848],[569,2721,2723,2763],{"className":2722},[852],[569,2724,2727,2741,2749],{"className":2725,"style":2726},[856],"height:0.8451em;",[569,2728,2729,2732],{"style":1894},[569,2730],{"className":2731,"style":1339},[864],[569,2733,2735],{"className":2734},[869,870,871,872],[569,2736,2738],{"className":2737},[612,872],[569,2739,1966],{"className":2740},[612,872],[569,2742,2743,2746],{"style":1348},[569,2744],{"className":2745,"style":1339},[864],[569,2747],{"className":2748,"style":1356},[1355],[569,2750,2751,2754],{"style":1917},[569,2752],{"className":2753,"style":1339},[864],[569,2755,2757],{"className":2756},[869,870,871,872],[569,2758,2760],{"className":2759},[612,872],[569,2761,1995],{"className":2762},[612,872],[569,2764,898],{"className":2765},[897],[569,2767,2769],{"className":2768},[852],[569,2770,2772],{"className":2771,"style":905},[856],[569,2773],{},[569,2775],{"className":2776},[911,1319],[569,2778],{"className":2779,"style":1128},[690],[569,2781,1176],{"className":2782},[1132],[569,2784],{"className":2785,"style":1128},[690],[569,2787,2789,2792,2795,2801],{"className":2788},[603],[569,2790],{"className":2791,"style":2596},[607],[569,2793,1221],{"className":2794},[612],[569,2796,2798],{"className":2797},[612],[569,2799,1190],{"className":2800},[1387],[569,2802,1108],{"className":2803},[612]," rote Kugeln, die Varianz ist ",[569,2806,2808,2857],{"className":2807},[572],[569,2809,2811],{"className":2810},[576],[578,2812,2813],{"xmlns":580},[582,2814,2815,2854],{},[585,2816,2817,2819,2821,2823,2825,2827,2829,2831,2834,2836,2839,2841,2849,2851],{},[588,2818,1196],{},[666,2820,802],{"stretchy":1169},[588,2822,758],{},[666,2824,813],{"stretchy":1169},[666,2826,1176],{},[1106,2828,2025],{},[666,2830,1181],{},[1106,2832,2833],{},"0,4",[666,2835,1181],{},[1106,2837,2838],{},"0,6",[666,2840,1181],{},[804,2842,2843,2846],{},[1106,2844,2845],{},"7",[1106,2847,2848],{},"9",[666,2850,1176],{},[1106,2852,2853],{},"0,56",[592,2855,2856],{"encoding":594},"V(X) = 3 \\cdot 0{,}4 \\cdot 0{,}6 \\cdot \\frac{7}{9} = 0{,}56",[569,2858,2860,2887,2905,2932,2959,3042],{"className":2859,"ariaHidden":599},[598],[569,2861,2863,2866,2869,2872,2875,2878,2881,2884],{"className":2862},[603],[569,2864],{"className":2865,"style":1264},[607],[569,2867,1196],{"className":2868,"style":691},[612,613],[569,2870,802],{"className":2871},[833],[569,2873,758],{"className":2874,"style":773},[612,613],[569,2876,813],{"className":2877},[911],[569,2879],{"className":2880,"style":1128},[690],[569,2882,1176],{"className":2883},[1132],[569,2885],{"className":2886,"style":1128},[690],[569,2888,2890,2893,2896,2899,2902],{"className":2889},[603],[569,2891],{"className":2892,"style":1142},[607],[569,2894,2025],{"className":2895},[612],[569,2897],{"className":2898,"style":691},[690],[569,2900,1181],{"className":2901},[695],[569,2903],{"className":2904,"style":691},[690],[569,2906,2908,2911,2914,2920,2923,2926,2929],{"className":2907},[603],[569,2909],{"className":2910,"style":2596},[607],[569,2912,2600],{"className":2913},[612],[569,2915,2917],{"className":2916},[612],[569,2918,1190],{"className":2919},[1387],[569,2921,1995],{"className":2922},[612],[569,2924],{"className":2925,"style":691},[690],[569,2927,1181],{"className":2928},[695],[569,2930],{"className":2931,"style":691},[690],[569,2933,2935,2938,2941,2947,2950,2953,2956],{"className":2934},[603],[569,2936],{"className":2937,"style":2596},[607],[569,2939,2600],{"className":2940},[612],[569,2942,2944],{"className":2943},[612],[569,2945,1190],{"className":2946},[1387],[569,2948,2126],{"className":2949},[612],[569,2951],{"className":2952,"style":691},[690],[569,2954,1181],{"className":2955},[695],[569,2957],{"className":2958,"style":691},[690],[569,2960,2962,2965,3033,3036,3039],{"className":2961},[603],[569,2963],{"className":2964,"style":2707},[607],[569,2966,2968,2971,3030],{"className":2967},[612],[569,2969],{"className":2970},[833,1319],[569,2972,2974],{"className":2973},[804],[569,2975,2977,3022],{"className":2976},[847,848],[569,2978,2980,3019],{"className":2979},[852],[569,2981,2983,2997,3005],{"className":2982,"style":2726},[856],[569,2984,2985,2988],{"style":1894},[569,2986],{"className":2987,"style":1339},[864],[569,2989,2991],{"className":2990},[869,870,871,872],[569,2992,2994],{"className":2993},[612,872],[569,2995,2848],{"className":2996},[612,872],[569,2998,2999,3002],{"style":1348},[569,3000],{"className":3001,"style":1339},[864],[569,3003],{"className":3004,"style":1356},[1355],[569,3006,3007,3010],{"style":1917},[569,3008],{"className":3009,"style":1339},[864],[569,3011,3013],{"className":3012},[869,870,871,872],[569,3014,3016],{"className":3015},[612,872],[569,3017,2845],{"className":3018},[612,872],[569,3020,898],{"className":3021},[897],[569,3023,3025],{"className":3024},[852],[569,3026,3028],{"className":3027,"style":905},[856],[569,3029],{},[569,3031],{"className":3032},[911,1319],[569,3034],{"className":3035,"style":1128},[690],[569,3037,1176],{"className":3038},[1132],[569,3040],{"className":3041,"style":1128},[690],[569,3043,3045,3048,3051,3057],{"className":3044},[603],[569,3046],{"className":3047,"style":2596},[607],[569,3049,2600],{"className":3050},[612],[569,3052,3054],{"className":3053},[612],[569,3055,1190],{"className":3056},[1387],[569,3058,3060],{"className":3059},[612],"56",[565,3062,3063,3064,3116,3117,3168,3169,3220,3221,3249],{},"Lotto „6 aus 49“: ",[569,3065,3067,3086],{"className":3066},[572],[569,3068,3070],{"className":3069},[576],[578,3071,3072],{"xmlns":580},[582,3073,3074,3083],{},[585,3075,3076,3078,3080],{},[588,3077,590],{},[666,3079,1176],{},[1106,3081,3082],{},"49",[592,3084,3085],{"encoding":594},"N = 49",[569,3087,3089,3107],{"className":3088,"ariaHidden":599},[598],[569,3090,3092,3095,3098,3101,3104],{"className":3091},[603],[569,3093],{"className":3094,"style":608},[607],[569,3096,590],{"className":3097,"style":614},[612,613],[569,3099],{"className":3100,"style":1128},[690],[569,3102,1176],{"className":3103},[1132],[569,3105],{"className":3106,"style":1128},[690],[569,3108,3110,3113],{"className":3109},[603],[569,3111],{"className":3112,"style":1142},[607],[569,3114,3082],{"className":3115},[612],", ",[569,3118,3120,3138],{"className":3119},[572],[569,3121,3123],{"className":3122},[576],[578,3124,3125],{"xmlns":580},[582,3126,3127,3135],{},[585,3128,3129,3131,3133],{},[588,3130,630],{},[666,3132,1176],{},[1106,3134,2126],{},[592,3136,3137],{"encoding":594},"M = 6",[569,3139,3141,3159],{"className":3140,"ariaHidden":599},[598],[569,3142,3144,3147,3150,3153,3156],{"className":3143},[603],[569,3145],{"className":3146,"style":608},[607],[569,3148,630],{"className":3149,"style":614},[612,613],[569,3151],{"className":3152,"style":1128},[690],[569,3154,1176],{"className":3155},[1132],[569,3157],{"className":3158,"style":1128},[690],[569,3160,3162,3165],{"className":3161},[603],[569,3163],{"className":3164,"style":1142},[607],[569,3166,2126],{"className":3167},[612]," Gewinnzahlen, ",[569,3170,3172,3190],{"className":3171},[572],[569,3173,3175],{"className":3174},[576],[578,3176,3177],{"xmlns":580},[582,3178,3179,3187],{},[585,3180,3181,3183,3185],{},[588,3182,723],{},[666,3184,1176],{},[1106,3186,2126],{},[592,3188,3189],{"encoding":594},"n = 6",[569,3191,3193,3211],{"className":3192,"ariaHidden":599},[598],[569,3194,3196,3199,3202,3205,3208],{"className":3195},[603],[569,3197],{"className":3198,"style":735},[607],[569,3200,723],{"className":3201},[612,613],[569,3203],{"className":3204,"style":1128},[690],[569,3206,1176],{"className":3207},[1132],[569,3209],{"className":3210,"style":1128},[690],[569,3212,3214,3217],{"className":3213},[603],[569,3215],{"className":3216,"style":1142},[607],[569,3218,2126],{"className":3219},[612]," Kreuze. Genau ",[569,3222,3224,3237],{"className":3223},[572],[569,3225,3227],{"className":3226},[576],[578,3228,3229],{"xmlns":580},[582,3230,3231,3235],{},[585,3232,3233],{},[1106,3234,2025],{},[592,3236,2025],{"encoding":594},[569,3238,3240],{"className":3239,"ariaHidden":599},[598],[569,3241,3243,3246],{"className":3242},[603],[569,3244],{"className":3245,"style":1142},[607],[569,3247,2025],{"className":3248},[612]," Richtige:",[569,3251,3253],{"className":3252},[1150],[569,3254,3256,3367],{"className":3255},[572],[569,3257,3259],{"className":3258},[576],[578,3260,3261],{"xmlns":580,"display":1159},[582,3262,3263,3364],{},[585,3264,3265,3267,3269,3271,3273,3275,3277,3279,3322,3324,3358,3361],{},[588,3266,2087],{},[666,3268,802],{"stretchy":1169},[588,3270,758],{},[666,3272,1176],{},[1106,3274,2025],{},[666,3276,813],{"stretchy":1169},[666,3278,1176],{},[804,3280,3281,3310],{},[585,3282,3283,3295,3297],{},[585,3284,3285,3287,3293],{},[666,3286,802],{"fence":599},[804,3288,3289,3291],{"linethickness":806},[1106,3290,2126],{},[1106,3292,2025],{},[666,3294,813],{"fence":599},[666,3296,1181],{},[585,3298,3299,3301,3308],{},[666,3300,802],{"fence":599},[804,3302,3303,3306],{"linethickness":806},[1106,3304,3305],{},"43",[1106,3307,2025],{},[666,3309,813],{"fence":599},[585,3311,3312,3314,3320],{},[666,3313,802],{"fence":599},[804,3315,3316,3318],{"linethickness":806},[1106,3317,3082],{},[1106,3319,2126],{},[666,3321,813],{"fence":599},[666,3323,1176],{},[804,3325,3326,3343],{},[585,3327,3328,3331,3333,3336,3340],{},[1106,3329,3330],{},"20",[666,3332,1181],{},[1106,3334,3335],{},"12",[3337,3338,3339],"mtext",{}," ",[1106,3341,3342],{},"341",[585,3344,3345,3348,3350,3353,3355],{},[1106,3346,3347],{},"13",[3337,3349,3339],{},[1106,3351,3352],{},"983",[3337,3354,3339],{},[1106,3356,3357],{},"816",[666,3359,3360],{},"≈",[1106,3362,3363],{},"0,0177",[592,3365,3366],{"encoding":594},"P(X = 3) = \\frac{\\binom{6}{3} \\cdot \\binom{43}{3}}{\\binom{49}{6}} = \\frac{20 \\cdot 12\\,341}{13\\,983\\,816} \\approx 0{,}0177",[569,3368,3370,3394,3415,3693,3800],{"className":3369,"ariaHidden":599},[598],[569,3371,3373,3376,3379,3382,3385,3388,3391],{"className":3372},[603],[569,3374],{"className":3375,"style":1264},[607],[569,3377,2087],{"className":3378,"style":2178},[612,613],[569,3380,802],{"className":3381},[833],[569,3383,758],{"className":3384,"style":773},[612,613],[569,3386],{"className":3387,"style":1128},[690],[569,3389,1176],{"className":3390},[1132],[569,3392],{"className":3393,"style":1128},[690],[569,3395,3397,3400,3403,3406,3409,3412],{"className":3396},[603],[569,3398],{"className":3399,"style":1264},[607],[569,3401,2025],{"className":3402},[612],[569,3404,813],{"className":3405},[911],[569,3407],{"className":3408,"style":1128},[690],[569,3410,1176],{"className":3411},[1132],[569,3413],{"className":3414,"style":1128},[690],[569,3416,3418,3421,3684,3687,3690],{"className":3417},[603],[569,3419],{"className":3420,"style":2221},[607],[569,3422,3424,3427,3681],{"className":3423},[612],[569,3425],{"className":3426},[833,1319],[569,3428,3430],{"className":3429},[804],[569,3431,3433,3673],{"className":3432},[847,848],[569,3434,3436,3670],{"className":3435},[852],[569,3437,3439,3513,3521],{"className":3438,"style":2240},[856],[569,3440,3441,3444],{"style":2243},[569,3442],{"className":3443,"style":1339},[864],[569,3445,3447],{"className":3446},[612],[569,3448,3450,3456,3507],{"className":3449},[612],[569,3451,3453],{"className":3452,"style":835},[833,834],[569,3454,802],{"className":3455},[839,840],[569,3457,3459],{"className":3458},[804],[569,3460,3462,3499],{"className":3461},[847,848],[569,3463,3465,3496],{"className":3464},[852],[569,3466,3468,3482],{"className":3467,"style":2271},[856],[569,3469,3470,3473],{"style":860},[569,3471],{"className":3472,"style":865},[864],[569,3474,3476],{"className":3475},[869,870,871,872],[569,3477,3479],{"className":3478},[612,872],[569,3480,2126],{"className":3481},[612,872],[569,3483,3484,3487],{"style":881},[569,3485],{"className":3486,"style":865},[864],[569,3488,3490],{"className":3489},[869,870,871,872],[569,3491,3493],{"className":3492},[612,872],[569,3494,3082],{"className":3495},[612,872],[569,3497,898],{"className":3498},[897],[569,3500,3502],{"className":3501},[852],[569,3503,3505],{"className":3504,"style":905},[856],[569,3506],{},[569,3508,3510],{"className":3509,"style":835},[911,834],[569,3511,813],{"className":3512},[839,840],[569,3514,3515,3518],{"style":1348},[569,3516],{"className":3517,"style":1339},[864],[569,3519],{"className":3520,"style":1356},[1355],[569,3522,3523,3526],{"style":2327},[569,3524],{"className":3525,"style":1339},[864],[569,3527,3529,3595,3598,3601,3604],{"className":3528},[612],[569,3530,3532,3538,3589],{"className":3531},[612],[569,3533,3535],{"className":3534,"style":835},[833,834],[569,3536,802],{"className":3537},[839,840],[569,3539,3541],{"className":3540},[804],[569,3542,3544,3581],{"className":3543},[847,848],[569,3545,3547,3578],{"className":3546},[852],[569,3548,3550,3564],{"className":3549,"style":2271},[856],[569,3551,3552,3555],{"style":860},[569,3553],{"className":3554,"style":865},[864],[569,3556,3558],{"className":3557},[869,870,871,872],[569,3559,3561],{"className":3560},[612,872],[569,3562,2025],{"className":3563},[612,872],[569,3565,3566,3569],{"style":881},[569,3567],{"className":3568,"style":865},[864],[569,3570,3572],{"className":3571},[869,870,871,872],[569,3573,3575],{"className":3574},[612,872],[569,3576,2126],{"className":3577},[612,872],[569,3579,898],{"className":3580},[897],[569,3582,3584],{"className":3583},[852],[569,3585,3587],{"className":3586,"style":905},[856],[569,3588],{},[569,3590,3592],{"className":3591,"style":835},[911,834],[569,3593,813],{"className":3594},[839,840],[569,3596],{"className":3597,"style":691},[690],[569,3599,1181],{"className":3600},[695],[569,3602],{"className":3603,"style":691},[690],[569,3605,3607,3613,3664],{"className":3606},[612],[569,3608,3610],{"className":3609,"style":835},[833,834],[569,3611,802],{"className":3612},[839,840],[569,3614,3616],{"className":3615},[804],[569,3617,3619,3656],{"className":3618},[847,848],[569,3620,3622,3653],{"className":3621},[852],[569,3623,3625,3639],{"className":3624,"style":2271},[856],[569,3626,3627,3630],{"style":860},[569,3628],{"className":3629,"style":865},[864],[569,3631,3633],{"className":3632},[869,870,871,872],[569,3634,3636],{"className":3635},[612,872],[569,3637,2025],{"className":3638},[612,872],[569,3640,3641,3644],{"style":881},[569,3642],{"className":3643,"style":865},[864],[569,3645,3647],{"className":3646},[869,870,871,872],[569,3648,3650],{"className":3649},[612,872],[569,3651,3305],{"className":3652},[612,872],[569,3654,898],{"className":3655},[897],[569,3657,3659],{"className":3658},[852],[569,3660,3662],{"className":3661,"style":905},[856],[569,3663],{},[569,3665,3667],{"className":3666,"style":835},[911,834],[569,3668,813],{"className":3669},[839,840],[569,3671,898],{"className":3672},[897],[569,3674,3676],{"className"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ist etwa jeder ",[569,3823,3825,3839],{"className":3824},[572],[569,3826,3828],{"className":3827},[576],[578,3829,3830],{"xmlns":580},[582,3831,3832,3837],{},[585,3833,3834],{},[1106,3835,3836],{},"57",[592,3838,3836],{"encoding":594},[569,3840,3842],{"className":3841,"ariaHidden":599},[598],[569,3843,3845,3848],{"className":3844},[603],[569,3846],{"className":3847,"style":1142},[607],[569,3849,3836],{"className":3850},[612],". Tipp.",[560,3853,3855],{"id":3854},"typische-fehler","Typische Fehler",[782,3857,3858,4133,4242],{},[785,3859,3860,3861,4094,4095,777],{},"Die Binomialverteilung verwenden, obwohl ohne Zurücklegen gezogen wird. Im Urnenbeispiel ergäbe ",[569,3862,3864,3906],{"className":3863},[572],[569,3865,3867],{"className":3866},[576],[578,3868,3869],{"xmlns":580},[582,3870,3871,3903],{},[585,3872,3873,3885,3887,3894,3896,3898,3900],{},[585,3874,3875,3877,3883],{},[666,3876,802],{"fence":599},[804,3878,3879,3881],{"linethickness":806},[1106,3880,2025],{},[1106,3882,1108],{},[666,3884,813],{"fence":599},[666,3886,1181],{},[3888,3889,3890,3892],"msup",{},[1106,3891,2833],{},[1106,3893,1108],{},[666,3895,1181],{},[1106,3897,2838],{},[666,3899,1176],{},[1106,3901,3902],{},"0,288",[592,3904,3905],{"encoding":594},"\\binom{3}{2} \\cdot 0{,}4^2 \\cdot 0{,}6 = 0{,}288",[569,3907,3909,3991,4048,4075],{"className":3908,"ariaHidden":599},[598],[569,3910,3912,3916,3982,3985,3988],{"className":3911},[603],[569,3913],{"className":3914,"style":3915},[607],"height:1.2451em;vertical-align:-0.35em;",[569,3917,3919,3925,3976],{"className":3918},[612],[569,3920,3922],{"className":3921,"style":835},[833,834],[569,3923,802],{"className":3924},[839,840],[569,3926,3928],{"className":3927},[804],[569,3929,3931,3968],{"className":3930},[847,848],[569,3932,3934,3965],{"className":3933},[852],[569,3935,3937,3951],{"className":3936,"style":2271},[856],[569,3938,3939,3942],{"style":860},[569,3940],{"className":3941,"style":865},[864],[569,3943,3945],{"className":3944},[869,870,871,872],[569,3946,3948],{"className":3947},[612,872],[569,3949,1108],{"className":3950},[612,872],[569,3952,3953,3956],{"style":881},[569,3954],{"className":3955,"style":865},[864],[569,3957,3959],{"className":3958},[869,870,871,872],[569,3960,3962],{"className":3961},[612,872],[569,3963,2025],{"className":3964},[612,872],[569,3966,898],{"className":3967},[897],[569,3969,3971],{"className":3970},[852],[569,3972,3974],{"className":3973,"style":905},[856],[569,3975],{},[569,3977,3979],{"className":3978,"style":835},[911,834],[569,3980,813],{"className":3981},[839,840],[569,3983],{"className":3984,"style":691},[690],[569,3986,1181],{"className":3987},[695],[569,3989],{"className":3990,"style":691},[690],[569,3992,3994,3998,4001,4007,4039,4042,4045],{"className":3993},[603],[569,3995],{"className":3996,"style":3997},[607],"height:1.0085em;vertical-align:-0.1944em;",[569,3999,2600],{"className":4000},[612],[569,4002,4004],{"className":4003},[612],[569,4005,1190],{"className":4006},[1387],[569,4008,4010,4013],{"className":4009},[612],[569,4011,1995],{"className":4012},[612],[569,4014,4017],{"className":4015},[4016],"msupsub",[569,4018,4020],{"className":4019},[847],[569,4021,4023],{"className":4022},[852],[569,4024,4027],{"className":4025,"style":4026},[856],"height:0.8141em;",[569,4028,4030,4033],{"style":4029},"top:-3.063em;margin-right:0.05em;",[569,4031],{"className":4032,"style":865},[864],[569,4034,4036],{"className":4035},[869,870,871,872],[569,4037,1108],{"className":4038},[612,872],[569,4040],{"className":4041,"style":691},[690],[569,4043,1181],{"className":4044},[695],[569,4046],{"className":4047,"style":691},[690],[569,4049,4051,4054,4057,4063,4066,4069,4072],{"className":4050},[603],[569,4052],{"className":4053,"style":2596},[607],[569,4055,2600],{"className":4056},[612],[569,4058,4060],{"className":4059},[612],[569,4061,1190],{"className":4062},[1387],[569,4064,2126],{"className":4065},[612],[569,4067],{"className":4068,"style":1128},[690],[569,4070,1176],{"className":4071},[1132],[569,4073],{"className":4074,"style":1128},[690],[569,4076,4078,4081,4084,4090],{"className":4077},[603],[569,4079],{"className":4080,"style":2596},[607],[569,4082,2600],{"className":4083},[612],[569,4085,4087],{"className":4086},[612],[569,4088,1190],{"className":4089},[1387],[569,4091,4093],{"className":4092},[612],"288"," statt ",[569,4096,4098,4112],{"className":4097},[572],[569,4099,4101],{"className":4100},[576],[578,4102,4103],{"xmlns":580},[582,4104,4105,4109],{},[585,4106,4107],{},[1106,4108,2162],{},[592,4110,4111],{"encoding":594},"0{,}3",[569,4113,4115],{"className":4114,"ariaHidden":599},[598],[569,4116,4118,4121,4124,4130],{"className":4117},[603],[569,4119],{"className":4120,"style":2596},[607],[569,4122,2600],{"className":4123},[612],[569,4125,4127],{"className":4126},[612],[569,4128,1190],{"className":4129},[1387],[569,4131,2025],{"className":4132},[612],[785,4134,4135,4136,4139,4140,4190,4191,4241],{},"Im zweiten Faktor des Zählers falsche Zahlen einsetzen. Es sind die ",[647,4137,4138],{},"Nieten",": ",[569,4141,4143,4160],{"className":4142},[572],[569,4144,4146],{"className":4145},[576],[578,4147,4148],{"xmlns":580},[582,4149,4150,4158],{},[585,4151,4152,4154,4156],{},[588,4153,590],{},[666,4155,668],{},[588,4157,630],{},[592,4159,673],{"encoding":594},[569,4161,4163,4181],{"className":4162,"ariaHidden":599},[598],[569,4164,4166,4169,4172,4175,4178],{"className":4165},[603],[569,4167],{"className":4168,"style":683},[607],[569,4170,590],{"className":4171,"style":614},[612,613],[569,4173],{"className":4174,"style":691},[690],[569,4176,668],{"className":4177},[695],[569,4179],{"className":4180,"style":691},[690],[569,4182,4184,4187],{"className":4183},[603],[569,4185],{"className":4186,"style":608},[607],[569,4188,630],{"className":4189,"style":614},[612,613]," Nieten, davon ",[569,4192,4194,4211],{"className":4193},[572],[569,4195,4197],{"className":4196},[576],[578,4198,4199],{"xmlns":580},[582,4200,4201,4209],{},[585,4202,4203,4205,4207],{},[588,4204,723],{},[666,4206,668],{},[588,4208,932],{},[592,4210,1002],{"encoding":594},[569,4212,4214,4232],{"className":4213,"ariaHidden":599},[598],[569,4215,4217,4220,4223,4226,4229],{"className":4216},[603],[569,4218],{"className":4219,"style":1012},[607],[569,4221,723],{"className":4222},[612,613],[569,4224],{"className":4225,"style":691},[690],[569,4227,668],{"className":4228},[695],[569,4230],{"className":4231,"style":691},[690],[569,4233,4235,4238],{"className":4234},[603],[569,4236],{"className":4237,"style":944},[607],[569,4239,932],{"className":4240,"style":948},[612,613]," gezogen.",[785,4243,4244,4272,4273,4301,4302,4330,4331,4359],{},[569,4245,4247,4260],{"className":4246},[572],[569,4248,4250],{"className":4249},[576],[578,4251,4252],{"xmlns":580},[582,4253,4254,4258],{},[585,4255,4256],{},[588,4257,630],{},[592,4259,630],{"encoding":594},[569,4261,4263],{"className":4262,"ariaHidden":599},[598],[569,4264,4266,4269],{"className":4265},[603],[569,4267],{"className":4268,"style":608},[607],[569,4270,630],{"className":4271,"style":614},[612,613]," und ",[569,4274,4276,4289],{"className":4275},[572],[569,4277,4279],{"className":4278},[576],[578,4280,4281],{"xmlns":580},[582,4282,4283,4287],{},[585,4284,4285],{},[588,4286,723],{},[592,4288,723],{"encoding":594},[569,4290,4292],{"className":4291,"ariaHidden":599},[598],[569,4293,4295,4298],{"className":4294},[603],[569,4296],{"className":4297,"style":735},[607],[569,4299,723],{"className":4300},[612,613]," verwechseln: ",[569,4303,4305,4318],{"className":4304},[572],[569,4306,4308],{"className":4307},[576],[578,4309,4310],{"xmlns":580},[582,4311,4312,4316],{},[585,4313,4314],{},[588,4315,630],{},[592,4317,630],{"encoding":594},[569,4319,4321],{"className":4320,"ariaHidden":599},[598],[569,4322,4324,4327],{"className":4323},[603],[569,4325],{"className":4326,"style":608},[607],[569,4328,630],{"className":4329,"style":614},[612,613]," ist, was in der Urne ist, ",[569,4332,4334,4347],{"className":4333},[572],[569,4335,4337],{"className":4336},[576],[578,4338,4339],{"xmlns":580},[582,4340,4341,4345],{},[585,4342,4343],{},[588,4344,723],{},[592,4346,723],{"encoding":594},[569,4348,4350],{"className":4349,"ariaHidden":599},[598],[569,4351,4353,4356],{"className":4352},[603],[569,4354],{"className":4355,"style":735},[607],[569,4357,723],{"className":4358},[612,613]," ist, was gezogen wird.",{"title":4361,"searchDepth":4362,"depth":4362,"links":4363},"",2,[4364,4365,4366],{"id":562,"depth":4362,"text":563},{"id":1947,"depth":4362,"text":1948},{"id":3854,"depth":4362,"text":3855},[4368,4370,4373,4375,4377,4380,4383,4385,4388,4391,4394,4396],{"lhs":4369,"rhs":1221},"(combinations(4,0)*combinations(6,3) + combinations(4,1)*combinations(6,2) + combinations(4,2)*combinations(6,1) + combinations(4,3)*combinations(6,0)) \u002F combinations(10,3)",{"lhs":4371,"rhs":4372},"combinations(4, 2) * combinations(6, 1) \u002F combinations(10, 3)","0.3",{"lhs":4374,"rhs":4372},"6 * 6 \u002F 120",{"lhs":4376,"rhs":2157},"combinations(10, 3)",{"lhs":4378,"rhs":4379},"3 * 4 \u002F 10","1.2",{"lhs":4381,"rhs":4382},"3 * 0.4 * 0.6 * 7 \u002F 9","0.56",{"lhs":4384,"rhs":4382},"(0*20 + 1*60 + 4*36 + 9*4) \u002F 120 - 1.2^2",{"lhs":4386,"rhs":4387},"combinations(6, 3) * combinations(43, 3)","20 * 12341",{"lhs":4389,"rhs":4390},"combinations(49, 6)","13983816",{"lhs":4392,"rhs":4393},"round(20 * 12341 \u002F 13983816, 4)","0.0177",{"lhs":4395,"rhs":3836},"round(13983816 \u002F (20 * 12341))",{"lhs":4397,"rhs":4398},"combinations(3, 2) * 0.4^2 * 0.6","0.288","0 \\leq M \\leq N,\\ 1 \\leq n \\leq N,\\ k \\in \\{0, 1, \\ldots, n\\},\\ \\binom{a}{b} = 0 \\text{ für } b > a","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>M\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 \\leq M \\leq N,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 \\leq n \\leq N,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmo stretchy=\"false\">{\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">}\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\{0, 1, \\ldots, n\\},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">{\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">}\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\binom{a}{b} = 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7454em;\">\u003Cspan style=\"top:-2.355em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.144em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b > a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","hypergeometric-distribution","P(X = k) = \\frac{\\binom{M}{k} \\cdot \\binom{N-M}{n-k}}{\\binom{N}{n}}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>M\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmrow>\u003Cmi>N\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>N\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X = k) = \\frac{\\binom{M}{k} \\cdot \\binom{N-M}{n-k}}{\\binom{N}{n}}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.878em;vertical-align:-1.1623em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.7157em;\">\u003Cspan style=\"top:-2.1877em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9223em;\">\u003Cspan style=\"top:-2.355em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.144em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.7933em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9223em;\">\u003Cspan style=\"top:-2.355em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.144em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9223em;\">\u003Cspan style=\"top:-2.355em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.144em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.4033em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1623em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fhypergeometrische-verteilung",[],[4412,4413,4414],"binomial-distribution","binomial-coefficient","laplace-probability",{"title":548,"description":4361},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fhypergeometrische-verteilung","Wahrscheinlichkeit für genau k Treffer, wenn man n Objekte ohne Zurücklegen aus N Objekten mit M Treffern zieht.",[4419,4420,4421,4422,4423],"ziehen ohne zurücklegen","urnenmodell","lotto","binomialkoeffizient","wahrscheinlichkeitsverteilung",[4425,4428,4431,4434,4437],{"symbol":758,"meaning":4426,"symbolHtml":4427},"Anzahl der gezogenen Treffer-Objekte","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":590,"meaning":4429,"symbolHtml":4430},"Gesamtzahl der Objekte in der Urne","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>N\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":630,"meaning":4432,"symbolHtml":4433},"Anzahl der Treffer-Objekte in der Urne, z.B. rote Kugeln","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">M\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":723,"meaning":4435,"symbolHtml":4436},"Anzahl der gezogenen Objekte (ohne Zurücklegen)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":932,"meaning":4438,"symbolHtml":4439},"gewünschte Anzahl an Treffern in der Stichprobe","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","nojoyN3H2r3hgmJFr3E1t_L_BdjWGbOi68F0MU6J59U",[4442,4445,4448],{"stem":4443,"title":4444,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialkoeffizient","Binomialkoeffizient",{"stem":4446,"title":4447,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":4449,"title":4450,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Flaplace-wahrscheinlichkeit","Laplace-Wahrscheinlichkeit",1793824285814]