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= \\frac{1}{p}, \\qquad V(X) = \\frac{1-p}{p^2}, \\qquad P(X > k) = (1-p)^k",[569,957,959,989,1107,1249,1270,1291],{"className":958,"ariaHidden":598},[597],[569,960,962,965,969,972,975,978,982,986],{"className":961},[602],[569,963],{"className":964,"style":778},[606],[569,966,868],{"className":967,"style":968},[611,612],"margin-right:0.0576em;",[569,970,760],{"className":971},[785],[569,973,628],{"className":974,"style":644},[611,612],[569,976,765],{"className":977},[792],[569,979],{"className":980,"style":981},[719],"margin-right:0.2778em;",[569,983,877],{"className":984},[985],"mrel",[569,987],{"className":988,"style":981},[719],[569,990,992,996,1074,1078,1082,1086,1089,1092,1095,1098,1101,1104],{"className":991},[602],[569,993],{"className":994,"style":995},[606],"height:2.2019em;vertical-align:-0.8804em;",[569,997,999,1003,1071],{"className":998},[611],[569,1000],{"className":1001},[785,1002],"nulldelimiter",[569,1004,1006],{"className":1005},[879],[569,1007,1011,1062],{"className":1008},[1009,1010],"vlist-t","vlist-t2",[569,1012,1015,1057],{"className":1013},[1014],"vlist-r",[569,1016,1020,1034,1045],{"className":1017,"style":1019},[1018],"vlist","height:1.3214em;",[569,1021,1023,1028],{"style":1022},"top:-2.314em;",[569,1024],{"className":1025,"style":1027},[1026],"pstrut","height:3em;",[569,1029,1031],{"className":1030},[611],[569,1032,565],{"className":1033},[611,612],[569,1035,1037,1040],{"style":1036},"top:-3.23em;",[569,1038],{"className":1039,"style":1027},[1026],[569,1041],{"className":1042,"style":1044},[1043],"frac-line","border-bottom-width:0.04em;",[569,1046,1048,1051],{"style":1047},"top:-3.677em;",[569,1049],{"className":1050,"style":1027},[1026],[569,1052,1054],{"className":1053},[611],[569,1055,699],{"className":1056},[611],[569,1058,1061],{"className":1059},[1060],"vlist-s","​",[569,1063,1065],{"className":1064},[1014],[569,1066,1069],{"className":1067,"style":1068},[1018],"height:0.8804em;",[569,1070],{},[569,1072],{"className":1073},[792,1002],[569,1075,887],{"className":1076},[1077],"mpunct",[569,1079],{"className":1080,"style":1081},[719],"margin-right:2em;",[569,1083],{"className":1084,"style":1085},[719],"margin-right:0.1667em;",[569,1087,756],{"className":1088,"style":720},[611,612],[569,1090,760],{"className":1091},[785],[569,1093,628],{"className":1094,"style":644},[611,612],[569,1096,765],{"className":1097},[792],[569,1099],{"className":1100,"style":981},[719],[569,1102,877],{"className":1103},[985],[569,1105],{"className":1106,"style":981},[719],[569,1108,1110,1113,1221,1224,1227,1230,1234,1237,1240,1243,1246],{"className":1109},[602],[569,1111],{"className":1112,"style":995},[606],[569,1114,1116,1119,1218],{"className":1115},[611],[569,1117],{"className":1118},[785,1002],[569,1120,1122],{"className":1121},[879],[569,1123,1125,1210],{"className":1124},[1009,1010],[569,1126,1128,1207],{"className":1127},[1014],[569,1129,1131,1176,1184],{"className":1130,"style":1019},[1018],[569,1132,1133,1136],{"style":1022},[569,1134],{"className":1135,"style":1027},[1026],[569,1137,1139],{"className":1138},[611],[569,1140,1142,1145],{"className":1141},[611],[569,1143,565],{"className":1144},[611,612],[569,1146,1149],{"className":1147},[1148],"msupsub",[569,1150,1152],{"className":1151},[1009],[569,1153,1155],{"className":1154},[1014],[569,1156,1159],{"className":1157,"style":1158},[1018],"height:0.7401em;",[569,1160,1162,1166],{"style":1161},"top:-2.989em;margin-right:0.05em;",[569,1163],{"className":1164,"style":1165},[1026],"height:2.7em;",[569,1167,1173],{"className":1168},[1169,1170,1171,1172],"sizing","reset-size6","size3","mtight",[569,1174,918],{"className":1175},[611,1172],[569,1177,1178,1181],{"style":1036},[569,1179],{"className":1180,"style":1027},[1026],[569,1182],{"className":1183,"style":1044},[1043],[569,1185,1186,1189],{"style":1047},[569,1187],{"className":1188,"style":1027},[1026],[569,1190,1192,1195,1198,1201,1204],{"className":1191},[611],[569,1193,699],{"className":1194},[611],[569,1196],{"className":1197,"style":720},[719],[569,1199,695],{"className":1200},[724],[569,1202],{"className":1203,"style":720},[719],[569,1205,565],{"className":1206},[611,612],[569,1208,1061],{"className":1209},[1060],[569,1211,1213],{"className":1212},[1014],[569,1214,1216],{"className":1215,"style":1068},[1018],[569,1217],{},[569,1219],{"className":1220},[792,1002],[569,1222,887],{"className":1223},[1077],[569,1225],{"className":1226,"style":1081},[719],[569,1228],{"className":1229,"style":1085},[719],[569,1231,925],{"className":1232,"style":1233},[611,612],"margin-right:0.1389em;",[569,1235,760],{"className":1236},[785],[569,1238,628],{"className":1239,"style":644},[611,612],[569,1241],{"className":1242,"style":981},[719],[569,1244,932],{"className":1245},[985],[569,1247],{"className":1248,"style":981},[719],[569,1250,1252,1255,1258,1261,1264,1267],{"className":1251},[602],[569,1253],{"className":1254,"style":778},[606],[569,1256,660],{"className":1257,"style":676},[611,612],[569,1259,765],{"className":1260},[792],[569,1262],{"className":1263,"style":981},[719],[569,1265,877],{"className":1266},[985],[569,1268],{"className":1269,"style":981},[719],[569,1271,1273,1276,1279,1282,1285,1288],{"className":1272},[602],[569,1274],{"className":1275,"style":778},[606],[569,1277,760],{"className":1278},[785],[569,1280,699],{"className":1281},[611],[569,1283],{"className":1284,"style":720},[719],[569,1286,695],{"className":1287},[724],[569,1289],{"className":1290,"style":720},[719],[569,1292,1294,1298,1301],{"className":1293},[602],[569,1295],{"className":1296,"style":1297},[606],"height:1.1491em;vertical-align:-0.25em;",[569,1299,565],{"className":1300},[611,612],[569,1302,1304,1307],{"className":1303},[792],[569,1305,765],{"className":1306},[792],[569,1308,1310],{"className":1309},[1148],[569,1311,1313],{"className":1312},[1009],[569,1314,1316],{"className":1315},[1014],[569,1317,1320],{"className":1318,"style":1319},[1018],"height:0.8991em;",[569,1321,1323,1326],{"style":1322},"top:-3.113em;margin-right:0.05em;",[569,1324],{"className":1325,"style":1165},[1026],[569,1327,1329],{"className":1328},[1169,1170,1171,1172],[569,1330,660],{"className":1331,"style":676},[611,612,1172],[565,1333,1334,1335,1339,1340,1536],{},"Die geometrische Verteilung ist ",[1336,1337,1338],"strong",{},"gedächtnislos",": ",[569,1341,1343,1396],{"className":1342},[572],[569,1344,1346],{"className":1345},[576],[578,1347,1348],{"xmlns":580},[582,1349,1350,1393],{},[585,1351,1352,1354,1356,1358,1360,1363,1366,1368,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391],{},[588,1353,925],{},[693,1355,760],{"stretchy":759},[588,1357,628],{},[693,1359,932],{},[588,1361,1362],{},"m",[693,1364,1365],{},"+",[588,1367,660],{},[693,1369,1370],{},"∣",[588,1372,628],{},[693,1374,932],{},[588,1376,1362],{},[693,1378,765],{"stretchy":759},[693,1380,877],{},[588,1382,925],{},[693,1384,760],{"stretchy":759},[588,1386,628],{},[693,1388,932],{},[588,1390,660],{},[693,1392,765],{"stretchy":759},[591,1394,1395],{"encoding":593},"P(X > m + k \\mid X > m) = P(X > k)",[569,1397,1399,1423,1442,1460,1479,1500,1524],{"className":1398,"ariaHidden":598},[597],[569,1400,1402,1405,1408,1411,1414,1417,1420],{"className":1401},[602],[569,1403],{"className":1404,"style":778},[606],[569,1406,925],{"className":1407,"style":1233},[611,612],[569,1409,760],{"className":1410},[785],[569,1412,628],{"className":1413,"style":644},[611,612],[569,1415],{"className":1416,"style":981},[719],[569,1418,932],{"className":1419},[985],[569,1421],{"className":1422,"style":981},[719],[569,1424,1426,1430,1433,1436,1439],{"className":1425},[602],[569,1427],{"className":1428,"style":1429},[606],"height:0.6667em;vertical-align:-0.0833em;",[569,1431,1362],{"className":1432},[611,612],[569,1434],{"className":1435,"style":720},[719],[569,1437,1365],{"className":1438},[724],[569,1440],{"className":1441,"style":720},[719],[569,1443,1445,1448,1451,1454,1457],{"className":1444},[602],[569,1446],{"className":1447,"style":778},[606],[569,1449,660],{"className":1450,"style":676},[611,612],[569,1452],{"className":1453,"style":981},[719],[569,1455,1370],{"className":1456},[985],[569,1458],{"className":1459,"style":981},[719],[569,1461,1463,1467,1470,1473,1476],{"className":1462},[602],[569,1464],{"className":1465,"style":1466},[606],"height:0.7224em;vertical-align:-0.0391em;",[569,1468,628],{"className":1469,"style":644},[611,612],[569,1471],{"className":1472,"style":981},[719],[569,1474,932],{"className":1475},[985],[569,1477],{"className":1478,"style":981},[719],[569,1480,1482,1485,1488,1491,1494,1497],{"className":1481},[602],[569,1483],{"className":1484,"style":778},[606],[569,1486,1362],{"className":1487},[611,612],[569,1489,765],{"className":1490},[792],[569,1492],{"className":1493,"style":981},[719],[569,1495,877],{"className":1496},[985],[569,1498],{"className":1499,"style":981},[719],[569,1501,1503,1506,1509,1512,1515,1518,1521],{"className":1502},[602],[569,1504],{"className":1505,"style":778},[606],[569,1507,925],{"className":1508,"style":1233},[611,612],[569,1510,760],{"className":1511},[785],[569,1513,628],{"className":1514,"style":644},[611,612],[569,1516],{"className":1517,"style":981},[719],[569,1519,932],{"className":1520},[985],[569,1522],{"className":1523,"style":981},[719],[569,1525,1527,1530,1533],{"className":1526},[602],[569,1528],{"className":1529,"style":778},[606],[569,1531,660],{"className":1532,"style":676},[611,612],[569,1534,765],{"className":1535},[792],". Wer schon lange wartet, hat dadurch keine besseren Chancen für die nächsten Versuche.",[565,1538,1539,1542,1543,1546,1547,1700,1701,1877,1878,2030,2031,2213],{},[1336,1540,1541],{},"Achtung, zwei Konventionen:"," Manche Bücher zählen statt der Versuchsnummer die Nieten ",[1336,1544,1545],{},"vor"," dem ersten Treffer, ",[569,1548,1550,1598],{"className":1549},[572],[569,1551,1553],{"className":1552},[576],[578,1554,1555],{"xmlns":580},[582,1556,1557,1595],{},[585,1558,1559,1562,1564,1566,1568,1570,1573,1576,1579,1581,1583,1585,1587,1589,1592],{},[588,1560,1561],{},"Y",[693,1563,877],{},[588,1565,628],{},[693,1567,695],{},[697,1569,699],{},[693,1571,1572],{},"∈",[693,1574,1575],{"stretchy":759},"{",[697,1577,1578],{},"0",[693,1580,887],{"separator":598},[697,1582,699],{},[693,1584,887],{"separator":598},[697,1586,918],{},[693,1588,887],{"separator":598},[693,1590,1591],{},"…",[693,1593,1594],{"stretchy":759},"}",[591,1596,1597],{"encoding":593},"Y = X - 1 \\in \\{0, 1, 2, \\ldots\\}",[569,1599,1601,1619,1638,1657],{"className":1600,"ariaHidden":598},[597],[569,1602,1604,1607,1610,1613,1616],{"className":1603},[602],[569,1605],{"className":1606,"style":640},[606],[569,1608,1561],{"className":1609,"style":720},[611,612],[569,1611],{"className":1612,"style":981},[719],[569,1614,877],{"className":1615},[985],[569,1617],{"className":1618,"style":981},[719],[569,1620,1622,1626,1629,1632,1635],{"className":1621},[602],[569,1623],{"className":1624,"style":1625},[606],"height:0.7667em;vertical-align:-0.0833em;",[569,1627,628],{"className":1628,"style":644},[611,612],[569,1630],{"className":1631,"style":720},[719],[569,1633,695],{"className":1634},[724],[569,1636],{"className":1637,"style":720},[719],[569,1639,1641,1645,1648,1651,1654],{"className":1640},[602],[569,1642],{"className":1643,"style":1644},[606],"height:0.6835em;vertical-align:-0.0391em;",[569,1646,699],{"className":1647},[611],[569,1649],{"className":1650,"style":981},[719],[569,1652,1572],{"className":1653},[985],[569,1655],{"className":1656,"style":981},[719],[569,1658,1660,1663,1666,1669,1672,1675,1678,1681,1684,1687,1690,1693,1697],{"className":1659},[602],[569,1661],{"className":1662,"style":778},[606],[569,1664,1575],{"className":1665},[785],[569,1667,1578],{"className":1668},[611],[569,1670,887],{"className":1671},[1077],[569,1673],{"className":1674,"style":1085},[719],[569,1676,699],{"className":1677},[611],[569,1679,887],{"className":1680},[1077],[569,1682],{"className":1683,"style":1085},[719],[569,1685,918],{"className":1686},[611],[569,1688,887],{"className":1689},[1077],[569,1691],{"className":1692,"style":1085},[719],[569,1694,1591],{"className":1695},[1696],"minner",[569,1698,1594],{"className":1699},[792],". Dann ist ",[569,1702,1704,1749],{"className":1703},[572],[569,1705,1707],{"className":1706},[576],[578,1708,1709],{"xmlns":580},[582,1710,1711,1746],{},[585,1712,1713,1715,1717,1719,1721,1723,1725,1727,1729,1731,1733,1735,1741,1744],{},[588,1714,925],{},[693,1716,760],{"stretchy":759},[588,1718,1561],{},[693,1720,877],{},[588,1722,660],{},[693,1724,765],{"stretchy":759},[693,1726,877],{},[693,1728,760],{"stretchy":759},[697,1730,699],{},[693,1732,695],{},[588,1734,565],{},[912,1736,1737,1739],{},[693,1738,765],{"stretchy":759},[588,1740,660],{},[693,1742,1743],{},"⋅",[588,1745,565],{},[591,1747,1748],{"encoding":593},"P(Y = k) = (1-p)^k \\cdot p",[569,1750,1752,1776,1797,1818,1868],{"className":1751,"ariaHidden":598},[597],[569,1753,1755,1758,1761,1764,1767,1770,1773],{"className":1754},[602],[569,1756],{"className":1757,"style":778},[606],[569,1759,925],{"className":1760,"style":1233},[611,612],[569,1762,760],{"className":1763},[785],[569,1765,1561],{"className":1766,"style":720},[611,612],[569,1768],{"className":1769,"style":981},[719],[569,1771,877],{"className":1772},[985],[569,1774],{"className":1775,"style":981},[719],[569,1777,1779,1782,1785,1788,1791,1794],{"className":1778},[602],[569,1780],{"className":1781,"style":778},[606],[569,1783,660],{"className":1784,"style":676},[611,612],[569,1786,765],{"className":1787},[792],[569,1789],{"className":1790,"style":981},[719],[569,1792,877],{"className":1793},[985],[569,1795],{"className":1796,"style":981},[719],[569,1798,1800,1803,1806,1809,1812,1815],{"className":1799},[602],[569,1801],{"className":1802,"style":778},[606],[569,1804,760],{"className":1805},[785],[569,1807,699],{"className":1808},[611],[569,1810],{"className":1811,"style":720},[719],[569,1813,695],{"className":1814},[724],[569,1816],{"className":1817,"style":720},[719],[569,1819,1821,1825,1828,1859,1862,1865],{"className":1820},[602],[569,1822],{"className":1823,"style":1824},[606],"height:1.0991em;vertical-align:-0.25em;",[569,1826,565],{"className":1827},[611,612],[569,1829,1831,1834],{"className":1830},[792],[569,1832,765],{"className":1833},[792],[569,1835,1837],{"className":1836},[1148],[569,1838,1840],{"className":1839},[1009],[569,1841,1843],{"className":1842},[1014],[569,1844,1847],{"className":1845,"style":1846},[1018],"height:0.8491em;",[569,1848,1850,1853],{"style":1849},"top:-3.063em;margin-right:0.05em;",[569,1851],{"className":1852,"style":1165},[1026],[569,1854,1856],{"className":1855},[1169,1170,1171,1172],[569,1857,660],{"className":1858,"style":676},[611,612,1172],[569,1860],{"className":1861,"style":720},[719],[569,1863,1743],{"className":1864},[724],[569,1866],{"className":1867,"style":720},[719],[569,1869,1871,1874],{"className":1870},[602],[569,1872],{"className":1873,"style":607},[606],[569,1875,565],{"className":1876},[611,612]," und ",[569,1879,1881,1915],{"className":1880},[572],[569,1882,1884],{"className":1883},[576],[578,1885,1886],{"xmlns":580},[582,1887,1888,1912],{},[585,1889,1890,1892,1894,1896,1898,1900],{},[588,1891,868],{},[693,1893,760],{"stretchy":759},[588,1895,1561],{},[693,1897,765],{"stretchy":759},[693,1899,877],{},[879,1901,1902,1910],{},[585,1903,1904,1906,1908],{},[697,1905,699],{},[693,1907,695],{},[588,1909,565],{},[588,1911,565],{},[591,1913,1914],{"encoding":593},"E(Y) = \\frac{1-p}{p}",[569,1916,1918,1945],{"className":1917,"ariaHidden":598},[597],[569,1919,1921,1924,1927,1930,1933,1936,1939,1942],{"className":1920},[602],[569,1922],{"className":1923,"style":778},[606],[569,1925,868],{"className":1926,"style":968},[611,612],[569,1928,760],{"className":1929},[785],[569,1931,1561],{"className":1932,"style":720},[611,612],[569,1934,765],{"className":1935},[792],[569,1937],{"className":1938,"style":981},[719],[569,1940,877],{"className":1941},[985],[569,1943],{"className":1944,"style":981},[719],[569,1946,1948,1952],{"className":1947},[602],[569,1949],{"className":1950,"style":1951},[606],"height:1.3783em;vertical-align:-0.4811em;",[569,1953,1955,1958,2027],{"className":1954},[611],[569,1956],{"className":1957},[785,1002],[569,1959,1961],{"className":1960},[879],[569,1962,1964,2018],{"className":1963},[1009,1010],[569,1965,1967,2015],{"className":1966},[1014],[569,1968,1971,1986,1994],{"className":1969,"style":1970},[1018],"height:0.8972em;",[569,1972,1974,1977],{"style":1973},"top:-2.655em;",[569,1975],{"className":1976,"style":1027},[1026],[569,1978,1980],{"className":1979},[1169,1170,1171,1172],[569,1981,1983],{"className":1982},[611,1172],[569,1984,565],{"className":1985},[611,612,1172],[569,1987,1988,1991],{"style":1036},[569,1989],{"className":1990,"style":1027},[1026],[569,1992],{"className":1993,"style":1044},[1043],[569,1995,1997,2000],{"style":1996},"top:-3.4461em;",[569,1998],{"className":1999,"style":1027},[1026],[569,2001,2003],{"className":2002},[1169,1170,1171,1172],[569,2004,2006,2009,2012],{"className":2005},[611,1172],[569,2007,699],{"className":2008},[611,1172],[569,2010,695],{"className":2011},[724,1172],[569,2013,565],{"className":2014},[611,612,1172],[569,2016,1061],{"className":2017},[1060],[569,2019,2021],{"className":2020},[1014],[569,2022,2025],{"className":2023,"style":2024},[1018],"height:0.4811em;",[569,2026],{},[569,2028],{"className":2029},[792,1002],". Die Varianz bleibt ",[569,2032,2034,2072],{"className":2033},[572],[569,2035,2037],{"className":2036},[576],[578,2038,2039],{"xmlns":580},[582,2040,2041,2069],{},[585,2042,2043,2045,2047,2049,2051,2053],{},[588,2044,756],{},[693,2046,760],{"stretchy":759},[588,2048,1561],{},[693,2050,765],{"stretchy":759},[693,2052,877],{},[879,2054,2055,2063],{},[585,2056,2057,2059,2061],{},[697,2058,699],{},[693,2060,695],{},[588,2062,565],{},[912,2064,2065,2067],{},[588,2066,565],{},[697,2068,918],{},[591,2070,2071],{"encoding":593},"V(Y) = \\frac{1-p}{p^2}",[569,2073,2075,2102],{"className":2074,"ariaHidden":598},[597],[569,2076,2078,2081,2084,2087,2090,2093,2096,2099],{"className":2077},[602],[569,2079],{"className":2080,"style":778},[606],[569,2082,756],{"className":2083,"style":720},[611,612],[569,2085,760],{"className":2086},[785],[569,2088,1561],{"className":2089,"style":720},[611,612],[569,2091,765],{"className":2092},[792],[569,2094],{"className":2095,"style":981},[719],[569,2097,877],{"className":2098},[985],[569,2100],{"className":2101,"style":981},[719],[569,2103,2105,2108],{"className":2104},[602],[569,2106],{"className":2107,"style":1951},[606],[569,2109,2111,2114,2210],{"className":2110},[611],[569,2112],{"className":2113},[785,1002],[569,2115,2117],{"className":2116},[879],[569,2118,2120,2202],{"className":2119},[1009,1010],[569,2121,2123,2199],{"className":2122},[1014],[569,2124,2126,2171,2179],{"className":2125,"style":1970},[1018],[569,2127,2128,2131],{"style":1973},[569,2129],{"className":2130,"style":1027},[1026],[569,2132,2134],{"className":2133},[1169,1170,1171,1172],[569,2135,2137],{"className":2136},[611,1172],[569,2138,2140,2143],{"className":2139},[611,1172],[569,2141,565],{"className":2142},[611,612,1172],[569,2144,2146],{"className":2145},[1148],[569,2147,2149],{"className":2148},[1009],[569,2150,2152],{"className":2151},[1014],[569,2153,2156],{"className":2154,"style":2155},[1018],"height:0.7463em;",[569,2157,2159,2163],{"style":2158},"top:-2.786em;margin-right:0.0714em;",[569,2160],{"className":2161,"style":2162},[1026],"height:2.5em;",[569,2164,2168],{"className":2165},[1169,2166,2167,1172],"reset-size3","size1",[569,2169,918],{"className":2170},[611,1172],[569,2172,2173,2176],{"style":1036},[569,2174],{"className":2175,"style":1027},[1026],[569,2177],{"className":2178,"style":1044},[1043],[569,2180,2181,2184],{"style":1996},[569,2182],{"className":2183,"style":1027},[1026],[569,2185,2187],{"className":2186},[1169,1170,1171,1172],[569,2188,2190,2193,2196],{"className":2189},[611,1172],[569,2191,699],{"className":2192},[611,1172],[569,2194,695],{"className":2195},[724,1172],[569,2197,565],{"className":2198},[611,612,1172],[569,2200,1061],{"className":2201},[1060],[569,2203,2205],{"className":2204},[1014],[569,2206,2208],{"className":2207,"style":2024},[1018],[569,2209],{},[569,2211],{"className":2212},[792,1002],".",[560,2215,2217],{"id":2216},"beispiele","Beispiele",[565,2219,2220,2221,2346],{},"Man würfelt, bis die erste Sechs fällt (",[569,2222,2224,2247],{"className":2223},[572],[569,2225,2227],{"className":2226},[576],[578,2228,2229],{"xmlns":580},[582,2230,2231,2244],{},[585,2232,2233,2235,2237],{},[588,2234,565],{},[693,2236,877],{},[879,2238,2239,2241],{},[697,2240,699],{},[697,2242,2243],{},"6",[591,2245,2246],{"encoding":593},"p = \\frac{1}{6}",[569,2248,2250,2268],{"className":2249,"ariaHidden":598},[597],[569,2251,2253,2256,2259,2262,2265],{"className":2252},[602],[569,2254],{"className":2255,"style":607},[606],[569,2257,565],{"className":2258},[611,612],[569,2260],{"className":2261,"style":981},[719],[569,2263,877],{"className":2264},[985],[569,2266],{"className":2267,"style":981},[719],[569,2269,2271,2275],{"className":2270},[602],[569,2272],{"className":2273,"style":2274},[606],"height:1.1901em;vertical-align:-0.345em;",[569,2276,2278,2281,2343],{"className":2277},[611],[569,2279],{"className":2280},[785,1002],[569,2282,2284],{"className":2283},[879],[569,2285,2287,2334],{"className":2286},[1009,1010],[569,2288,2290,2331],{"className":2289},[1014],[569,2291,2294,2308,2316],{"className":2292,"style":2293},[1018],"height:0.8451em;",[569,2295,2296,2299],{"style":1973},[569,2297],{"className":2298,"style":1027},[1026],[569,2300,2302],{"className":2301},[1169,1170,1171,1172],[569,2303,2305],{"className":2304},[611,1172],[569,2306,2243],{"className":2307},[611,1172],[569,2309,2310,2313],{"style":1036},[569,2311],{"className":2312,"style":1027},[1026],[569,2314],{"className":2315,"style":1044},[1043],[569,2317,2319,2322],{"style":2318},"top:-3.394em;",[569,2320],{"className":2321,"style":1027},[1026],[569,2323,2325],{"className":2324},[1169,1170,1171,1172],[569,2326,2328],{"className":2327},[611,1172],[569,2329,699],{"className":2330},[611,1172],[569,2332,1061],{"className":2333},[1060],[569,2335,2337],{"className":2336},[1014],[569,2338,2341],{"className":2339,"style":2340},[1018],"height:0.345em;",[569,2342],{},[569,2344],{"className":2345},[792,1002],"). Erste Sechs genau im dritten Wurf:",[569,2348,2350],{"className":2349},[852],[569,2351,2353,2421],{"className":2352},[572],[569,2354,2356],{"className":2355},[576],[578,2357,2358],{"xmlns":580,"display":861},[582,2359,2360,2418],{},[585,2361,2362,2364,2366,2368,2370,2373,2375,2377,2394,2396,2402,2404,2412,2415],{},[588,2363,925],{},[693,2365,760],{"stretchy":759},[588,2367,628],{},[693,2369,877],{},[697,2371,2372],{},"3",[693,2374,765],{"stretchy":759},[693,2376,877],{},[912,2378,2379,2392],{},[585,2380,2381,2383,2390],{},[693,2382,760],{"fence":598},[879,2384,2385,2388],{},[697,2386,2387],{},"5",[697,2389,2243],{},[693,2391,765],{"fence":598},[697,2393,918],{},[693,2395,1743],{},[879,2397,2398,2400],{},[697,2399,699],{},[697,2401,2243],{},[693,2403,877],{},[879,2405,2406,2409],{},[697,2407,2408],{},"25",[697,2410,2411],{},"216",[693,2413,2414],{},"≈",[697,2416,2417],{},"0,1157",[591,2419,2420],{"encoding":593},"P(X = 3) = \\left(\\frac{5}{6}\\right)^2 \\cdot \\frac{1}{6} = \\frac{25}{216} \\approx 0{,}1157",[569,2422,2424,2448,2469,2594,2672,2749],{"className":2423,"ariaHidden":598},[597],[569,2425,2427,2430,2433,2436,2439,2442,2445],{"className":2426},[602],[569,2428],{"className":2429,"style":778},[606],[569,2431,925],{"className":2432,"style":1233},[611,612],[569,2434,760],{"className":2435},[785],[569,2437,628],{"className":2438,"style":644},[611,612],[569,2440],{"className":2441,"style":981},[719],[569,2443,877],{"className":2444},[985],[569,2446],{"className":2447,"style":981},[719],[569,2449,2451,2454,2457,2460,2463,2466],{"className":2450},[602],[569,2452],{"className":2453,"style":778},[606],[569,2455,2372],{"className":2456},[611],[569,2458,765],{"className":2459},[792],[569,2461],{"className":2462,"style":981},[719],[569,2464,877],{"className":2465},[985],[569,2467],{"className":2468,"style":981},[719],[569,2470,2472,2476,2585,2588,2591],{"className":2471},[602],[569,2473],{"className":2474,"style":2475},[606],"height:2.604em;vertical-align:-0.95em;",[569,2477,2479,2560],{"className":2478},[1696],[569,2480,2482,2491,2554],{"className":2481},[1696],[569,2483,2487],{"className":2484,"style":2486},[785,2485],"delimcenter","top:0em;",[569,2488,760],{"className":2489},[2490,1171],"delimsizing",[569,2492,2494,2497,2551],{"className":2493},[611],[569,2495],{"className":2496},[785,1002],[569,2498,2500],{"className":2499},[879],[569,2501,2503,2542],{"className":2502},[1009,1010],[569,2504,2506,2539],{"className":2505},[1014],[569,2507,2509,2520,2528],{"className":2508,"style":1019},[1018],[569,2510,2511,2514],{"style":1022},[569,2512],{"className":2513,"style":1027},[1026],[569,2515,2517],{"className":2516},[611],[569,2518,2243],{"className":2519},[611],[569,2521,2522,2525],{"style":1036},[569,2523],{"className":2524,"style":1027},[1026],[569,2526],{"className":2527,"style":1044},[1043],[569,2529,2530,2533],{"style":1047},[569,2531],{"className":2532,"style":1027},[1026],[569,2534,2536],{"className":2535},[611],[569,2537,2387],{"className":2538},[611],[569,2540,1061],{"className":2541},[1060],[569,2543,2545],{"className":2544},[1014],[569,2546,2549],{"className":2547,"style":2548},[1018],"height:0.686em;",[569,2550],{},[569,2552],{"className":2553},[792,1002],[569,2555,2557],{"className":2556,"style":2486},[792,2485],[569,2558,765],{"className":2559},[2490,1171],[569,2561,2563],{"className":2562},[1148],[569,2564,2566],{"className":2565},[1009],[569,2567,2569],{"className":2568},[1014],[569,2570,2573],{"className":2571,"style":2572},[1018],"height:1.654em;",[569,2574,2576,2579],{"style":2575},"top:-3.9029em;margin-right:0.05em;",[569,2577],{"className":2578,"style":1165},[1026],[569,2580,2582],{"className":2581},[1169,1170,1171,1172],[569,2583,918],{"className":2584},[611,1172],[569,2586],{"className":2587,"style":720},[719],[569,2589,1743],{"className":2590},[724],[569,2592],{"className":2593,"style":720},[719],[569,2595,2597,2601,2663,2666,2669],{"className":2596},[602],[569,2598],{"className":2599,"style":2600},[606],"height:2.0074em;vertical-align:-0.686em;",[569,2602,2604,2607,2660],{"className":2603},[611],[569,2605],{"className":2606},[785,1002],[569,2608,2610],{"className":2609},[879],[569,2611,2613,2652],{"className":2612},[1009,1010],[569,2614,2616,2649],{"className":2615},[1014],[569,2617,2619,2630,2638],{"className":2618,"style":1019},[1018],[569,2620,2621,2624],{"style":1022},[569,2622],{"className":2623,"style":1027},[1026],[569,2625,2627],{"className":2626},[611],[569,2628,2243],{"className":2629},[611],[569,2631,2632,2635],{"style":1036},[569,2633],{"className":2634,"style":1027},[1026],[569,2636],{"className":2637,"style":1044},[1043],[569,2639,2640,2643],{"style":1047},[569,2641],{"className":2642,"style":1027},[1026],[569,2644,2646],{"className":2645},[611],[569,2647,699],{"className":2648},[611],[569,2650,1061],{"className":2651},[1060],[569,2653,2655],{"className":2654},[1014],[569,2656,2658],{"className":2657,"style":2548},[1018],[569,2659],{},[569,2661],{"className":2662},[792,1002],[569,2664],{"className":2665,"style":981},[719],[569,2667,877],{"className":2668},[985],[569,2670],{"className":2671,"style":981},[719],[569,2673,2675,2678,2740,2743,2746],{"className":2674},[602],[569,2676],{"className":2677,"style":2600},[606],[569,2679,2681,2684,2737],{"className":2680},[611],[569,2682],{"className":2683},[785,1002],[569,2685,2687],{"className":2686},[879],[569,2688,2690,2729],{"className":2689},[1009,1010],[569,2691,2693,2726],{"className":2692},[1014],[569,2694,2696,2707,2715],{"className":2695,"style":1019},[1018],[569,2697,2698,2701],{"style":1022},[569,2699],{"className":2700,"style":1027},[1026],[569,2702,2704],{"className":2703},[611],[569,2705,2411],{"className":2706},[611],[569,2708,2709,2712],{"style":1036},[569,2710],{"className":2711,"style":1027},[1026],[569,2713],{"className":2714,"style":1044},[1043],[569,2716,2717,2720],{"style":1047},[569,2718],{"className":2719,"style":1027},[1026],[569,2721,2723],{"className":2722},[611],[569,2724,2408],{"className":2725},[611],[569,2727,1061],{"className":2728},[1060],[569,2730,2732],{"className":2731},[1014],[569,2733,2735],{"className":2734,"style":2548},[1018],[569,2736],{},[569,2738],{"className":2739},[792,1002],[569,2741],{"className":2742,"style":981},[719],[569,2744,2414],{"className":2745},[985],[569,2747],{"className":2748,"style":981},[719],[569,2750,2752,2756,2759,2765],{"className":2751},[602],[569,2753],{"className":2754,"style":2755},[606],"height:0.8389em;vertical-align:-0.1944em;",[569,2757,1578],{"className":2758},[611],[569,2760,2762],{"className":2761},[611],[569,2763,887],{"className":2764},[1077],[569,2766,2768],{"className":2767},[611],"1157",[565,2770,2771,2772,2939,2940,3117,3118,3147,3148,2213],{},"Im Mittel braucht man ",[569,2773,2775,2814],{"className":2774},[572],[569,2776,2778],{"className":2777},[576],[578,2779,2780],{"xmlns":580},[582,2781,2782,2811],{},[585,2783,2784,2786,2788,2790,2792,2794,2807,2809],{},[588,2785,868],{},[693,2787,760],{"stretchy":759},[588,2789,628],{},[693,2791,765],{"stretchy":759},[693,2793,877],{},[879,2795,2796,2798],{},[697,2797,699],{},[585,2799,2800,2802,2805],{},[697,2801,699],{},[588,2803,2804],{"mathvariant":808},"\u002F",[697,2806,2243],{},[693,2808,877],{},[697,2810,2243],{},[591,2812,2813],{"encoding":593},"E(X) = \\frac{1}{1\u002F6} = 6",[569,2815,2817,2844,2930],{"className":2816,"ariaHidden":598},[597],[569,2818,2820,2823,2826,2829,2832,2835,2838,2841],{"className":2819},[602],[569,2821],{"className":2822,"style":778},[606],[569,2824,868],{"className":2825,"style":968},[611,612],[569,2827,760],{"className":2828},[785],[569,2830,628],{"className":2831,"style":644},[611,612],[569,2833,765],{"className":2834},[792],[569,2836],{"className":2837,"style":981},[719],[569,2839,877],{"className":2840},[985],[569,2842],{"className":2843,"style":981},[719],[569,2845,2847,2851,2921,2924,2927],{"className":2846},[602],[569,2848],{"className":2849,"style":2850},[606],"height:1.3651em;vertical-align:-0.52em;",[569,2852,2854,2857,2918],{"className":2853},[611],[569,2855],{"className":2856},[785,1002],[569,2858,2860],{"className":2859},[879],[569,2861,2863,2909],{"className":2862},[1009,1010],[569,2864,2866,2906],{"className":2865},[1014],[569,2867,2869,2884,2892],{"className":2868,"style":2293},[1018],[569,2870,2871,2874],{"style":1973},[569,2872],{"className":2873,"style":1027},[1026],[569,2875,2877],{"className":2876},[1169,1170,1171,1172],[569,2878,2880],{"className":2879},[611,1172],[569,2881,2883],{"className":2882},[611,1172],"1\u002F6",[569,2885,2886,2889],{"style":1036},[569,2887],{"className":2888,"style":1027},[1026],[569,2890],{"className":2891,"style":1044},[1043],[569,2893,2894,2897],{"style":2318},[569,2895],{"className":2896,"style":1027},[1026],[569,2898,2900],{"className":2899},[1169,1170,1171,1172],[569,2901,2903],{"className":2902},[611,1172],[569,2904,699],{"className":2905},[611,1172],[569,2907,1061],{"className":2908},[1060],[569,2910,2912],{"className":2911},[1014],[569,2913,2916],{"className":2914,"style":2915},[1018],"height:0.52em;",[569,2917],{},[569,2919],{"className":2920},[792,1002],[569,2922],{"className":2923,"style":981},[719],[569,2925,877],{"className":2926},[985],[569,2928],{"className":2929,"style":981},[719],[569,2931,2933,2936],{"className":2932},[602],[569,2934],{"className":2935,"style":734},[606],[569,2937,2243],{"className":2938},[611]," Würfe, die Varianz ist ",[569,2941,2943,2986],{"className":2942},[572],[569,2944,2946],{"className":2945},[576],[578,2947,2948],{"xmlns":580},[582,2949,2950,2983],{},[585,2951,2952,2978,2980],{},[879,2953,2954,2962],{},[585,2955,2956,2958,2960],{},[697,2957,2387],{},[588,2959,2804],{"mathvariant":808},[697,2961,2243],{},[585,2963,2964,2966,2968,2970,2972],{},[693,2965,760],{"stretchy":759},[697,2967,699],{},[588,2969,2804],{"mathvariant":808},[697,2971,2243],{},[912,2973,2974,2976],{},[693,2975,765],{"stretchy":759},[697,2977,918],{},[693,2979,877],{},[697,2981,2982],{},"30",[591,2984,2985],{"encoding":593},"\\frac{5\u002F6}{(1\u002F6)^2} = 30",[569,2987,2989,3108],{"className":2988,"ariaHidden":598},[597],[569,2990,2992,2996,3099,3102,3105],{"className":2991},[602],[569,2993],{"className":2994,"style":2995},[606],"height:1.53em;vertical-align:-0.52em;",[569,2997,2999,3002,3096],{"className":2998},[611],[569,3000],{"className":3001},[785,1002],[569,3003,3005],{"className":3004},[879],[569,3006,3008,3088],{"className":3007},[1009,1010],[569,3009,3011,3085],{"className":3010},[1014],[569,3012,3015,3061,3069],{"className":3013,"style":3014},[1018],"height:1.01em;",[569,3016,3017,3020],{"style":1973},[569,3018],{"className":3019,"style":1027},[1026],[569,3021,3023],{"className":3022},[1169,1170,1171,1172],[569,3024,3026,3029,3032],{"className":3025},[611,1172],[569,3027,760],{"className":3028},[785,1172],[569,3030,2883],{"className":3031},[611,1172],[569,3033,3035,3038],{"className":3034},[792,1172],[569,3036,765],{"className":3037},[792,1172],[569,3039,3041],{"className":3040},[1148],[569,3042,3044],{"className":3043},[1009],[569,3045,3047],{"className":3046},[1014],[569,3048,3050],{"className":3049,"style":2155},[1018],[569,3051,3052,3055],{"style":2158},[569,3053],{"className":3054,"style":2162},[1026],[569,3056,3058],{"className":3057},[1169,2166,2167,1172],[569,3059,918],{"className":3060},[611,1172],[569,3062,3063,3066],{"style":1036},[569,3064],{"className":3065,"style":1027},[1026],[569,3067],{"className":3068,"style":1044},[1043],[569,3070,3072,3075],{"style":3071},"top:-3.485em;",[569,3073],{"className":3074,"style":1027},[1026],[569,3076,3078],{"className":3077},[1169,1170,1171,1172],[569,3079,3081],{"className":3080},[611,1172],[569,3082,3084],{"className":3083},[611,1172],"5\u002F6",[569,3086,1061],{"className":3087},[1060],[569,3089,3091],{"className":3090},[1014],[569,3092,3094],{"className":3093,"style":2915},[1018],[569,3095],{},[569,3097],{"className":3098},[792,1002],[569,3100],{"className":3101,"style":981},[719],[569,3103,877],{"className":3104},[985],[569,3106],{"className":3107,"style":981},[719],[569,3109,3111,3114],{"className":3110},[602],[569,3112],{"className":3113,"style":734},[606],[569,3115,2982],{"className":3116},[611],". Nach ",[569,3119,3121,3135],{"className":3120},[572],[569,3122,3124],{"className":3123},[576],[578,3125,3126],{"xmlns":580},[582,3127,3128,3133],{},[585,3129,3130],{},[697,3131,3132],{},"10",[591,3134,3132],{"encoding":593},[569,3136,3138],{"className":3137,"ariaHidden":598},[597],[569,3139,3141,3144],{"className":3140},[602],[569,3142],{"className":3143,"style":734},[606],[569,3145,3132],{"className":3146},[611]," Würfen ist noch immer keine Sechs gefallen mit Wahrscheinlichkeit ",[569,3149,3151,3184],{"className":3150},[572],[569,3152,3154],{"className":3153},[576],[578,3155,3156],{"xmlns":580},[582,3157,3158,3181],{},[585,3159,3160,3176,3178],{},[912,3161,3162,3174],{},[585,3163,3164,3166,3172],{},[693,3165,760],{"fence":598},[879,3167,3168,3170],{},[697,3169,2387],{},[697,3171,2243],{},[693,3173,765],{"fence":598},[697,3175,3132],{},[693,3177,2414],{},[697,3179,3180],{},"0,1615",[591,3182,3183],{"encoding":593},"\\left(\\frac{5}{6}\\right)^{10} \\approx 0{,}1615",[569,3185,3187,3317],{"className":3186,"ariaHidden":598},[597],[569,3188,3190,3194,3308,3311,3314],{"className":3189},[602],[569,3191],{"className":3192,"style":3193},[606],"height:1.404em;vertical-align:-0.35em;",[569,3195,3197,3280],{"className":3196},[1696],[569,3198,3200,3206,3274],{"className":3199},[1696],[569,3201,3203],{"className":3202,"style":2486},[785,2485],[569,3204,760],{"className":3205},[2490,2167],[569,3207,3209,3212,3271],{"className":3208},[611],[569,3210],{"className":3211},[785,1002],[569,3213,3215],{"className":3214},[879],[569,3216,3218,3263],{"className":3217},[1009,1010],[569,3219,3221,3260],{"className":3220},[1014],[569,3222,3224,3238,3246],{"className":3223,"style":2293},[1018],[569,3225,3226,3229],{"style":1973},[569,3227],{"className":3228,"style":1027},[1026],[569,3230,3232],{"className":3231},[1169,1170,1171,1172],[569,3233,3235],{"className":3234},[611,1172],[569,3236,2243],{"className":3237},[611,1172],[569,3239,3240,3243],{"style":1036},[569,3241],{"className":3242,"style":1027},[1026],[569,3244],{"className":3245,"style":1044},[1043],[569,3247,3248,3251],{"style":2318},[569,3249],{"className":3250,"style":1027},[1026],[569,3252,3254],{"className":3253},[1169,1170,1171,1172],[569,3255,3257],{"className":3256},[611,1172],[569,3258,2387],{"className":3259},[611,1172],[569,3261,1061],{"className":3262},[1060],[569,3264,3266],{"className":3265},[1014],[569,3267,3269],{"className":3268,"style":2340},[1018],[569,3270],{},[569,3272],{"className":3273},[792,1002],[569,3275,3277],{"className":3276,"style":2486},[792,2485],[569,3278,765],{"className":3279},[2490,2167],[569,3281,3283],{"className":3282},[1148],[569,3284,3286],{"className":3285},[1009],[569,3287,3289],{"className":3288},[1014],[569,3290,3293],{"className":3291,"style":3292},[1018],"height:1.054em;",[569,3294,3296,3299],{"style":3295},"top:-3.3029em;margin-right:0.05em;",[569,3297],{"className":3298,"style":1165},[1026],[569,3300,3302],{"className":3301},[1169,1170,1171,1172],[569,3303,3305],{"className":3304},[611,1172],[569,3306,3132],{"className":3307},[611,1172],[569,3309],{"className":3310,"style":981},[719],[569,3312,2414],{"className":3313},[985],[569,3315],{"className":3316,"style":981},[719],[569,3318,3320,3323,3326,3332],{"className":3319},[602],[569,3321],{"className":3322,"style":2755},[606],[569,3324,1578],{"className":3325},[611],[569,3327,3329],{"className":3328},[611],[569,3330,887],{"className":3331},[1077],[569,3333,3335],{"className":3334},[611],"1615",[565,3337,3338,3339,3401,3402,3431,3432,3626,3627,3794,3795,2213],{},"Ein Los gewinnt mit ",[569,3340,3342,3361],{"className":3341},[572],[569,3343,3345],{"className":3344},[576],[578,3346,3347],{"xmlns":580},[582,3348,3349,3358],{},[585,3350,3351,3353,3355],{},[588,3352,565],{},[693,3354,877],{},[697,3356,3357],{},"0,05",[591,3359,3360],{"encoding":593},"p = 0{,}05",[569,3362,3364,3382],{"className":3363,"ariaHidden":598},[597],[569,3365,3367,3370,3373,3376,3379],{"className":3366},[602],[569,3368],{"className":3369,"style":607},[606],[569,3371,565],{"className":3372},[611,612],[569,3374],{"className":3375,"style":981},[719],[569,3377,877],{"className":3378},[985],[569,3380],{"className":3381,"style":981},[719],[569,3383,3385,3388,3391,3397],{"className":3384},[602],[569,3386],{"className":3387,"style":2755},[606],[569,3389,1578],{"className":3390},[611],[569,3392,3394],{"className":3393},[611],[569,3395,887],{"className":3396},[1077],[569,3398,3400],{"className":3399},[611],"05",". Wahrscheinlichkeit, unter den ersten ",[569,3403,3405,3419],{"className":3404},[572],[569,3406,3408],{"className":3407},[576],[578,3409,3410],{"xmlns":580},[582,3411,3412,3417],{},[585,3413,3414],{},[697,3415,3416],{},"20",[591,3418,3416],{"encoding":593},[569,3420,3422],{"className":3421,"ariaHidden":598},[597],[569,3423,3425,3428],{"className":3424},[602],[569,3426],{"className":3427,"style":734},[606],[569,3429,3416],{"className":3430},[611]," Losen mindestens einen Gewinn zu haben: ",[569,3433,3435,3478],{"className":3434},[572],[569,3436,3438],{"className":3437},[576],[578,3439,3440],{"xmlns":580},[582,3441,3442,3475],{},[585,3443,3444,3446,3448,3450,3453,3455,3457,3459,3461,3463,3470,3472],{},[588,3445,925],{},[693,3447,760],{"stretchy":759},[588,3449,628],{},[693,3451,3452],{},"≤",[697,3454,3416],{},[693,3456,765],{"stretchy":759},[693,3458,877],{},[697,3460,699],{},[693,3462,695],{},[912,3464,3465,3468],{},[697,3466,3467],{},"0,95",[697,3469,3416],{},[693,3471,2414],{},[697,3473,3474],{},"0,6415",[591,3476,3477],{"encoding":593},"P(X \\leq 20) = 1 - 0{,}95^{20} \\approx 0{,}6415",[569,3479,3481,3505,3526,3545,3607],{"className":3480,"ariaHidden":598},[597],[569,3482,3484,3487,3490,3493,3496,3499,3502],{"className":3483},[602],[569,3485],{"className":3486,"style":778},[606],[569,3488,925],{"className":3489,"style":1233},[611,612],[569,3491,760],{"className":3492},[785],[569,3494,628],{"className":3495,"style":644},[611,612],[569,3497],{"className":3498,"style":981},[719],[569,3500,3452],{"className":3501},[985],[569,3503],{"className":3504,"style":981},[719],[569,3506,3508,3511,3514,3517,3520,3523],{"className":3507},[602],[569,3509],{"className":3510,"style":778},[606],[569,3512,3416],{"className":3513},[611],[569,3515,765],{"className":3516},[792],[569,3518],{"className":3519,"style":981},[719],[569,3521,877],{"className":3522},[985],[569,3524],{"className":3525,"style":981},[719],[569,3527,3529,3533,3536,3539,3542],{"className":3528},[602],[569,3530],{"className":3531,"style":3532},[606],"height:0.7278em;vertical-align:-0.0833em;",[569,3534,699],{"className":3535},[611],[569,3537],{"className":3538,"style":720},[719],[569,3540,695],{"className":3541},[724],[569,3543],{"className":3544,"style":720},[719],[569,3546,3548,3552,3555,3561,3565,3598,3601,3604],{"className":3547},[602],[569,3549],{"className":3550,"style":3551},[606],"height:1.0085em;vertical-align:-0.1944em;",[569,3553,1578],{"className":3554},[611],[569,3556,3558],{"className":3557},[611],[569,3559,887],{"className":3560},[1077],[569,3562,3564],{"className":3563},[611],"9",[569,3566,3568,3571],{"className":3567},[611],[569,3569,2387],{"className":3570},[611],[569,3572,3574],{"className":3573},[1148],[569,3575,3577],{"className":3576},[1009],[569,3578,3580],{"className":3579},[1014],[569,3581,3584],{"className":3582,"style":3583},[1018],"height:0.8141em;",[569,3585,3586,3589],{"style":1849},[569,3587],{"className":3588,"style":1165},[1026],[569,3590,3592],{"className":3591},[1169,1170,1171,1172],[569,3593,3595],{"className":3594},[611,1172],[569,3596,3416],{"className":3597},[611,1172],[569,3599],{"className":3600,"style":981},[719],[569,3602,2414],{"className":3603},[985],[569,3605],{"className":3606,"style":981},[719],[569,3608,3610,3613,3616,3622],{"className":3609},[602],[569,3611],{"className":3612,"style":2755},[606],[569,3614,1578],{"className":3615},[611],[569,3617,3619],{"className":3618},[611],[569,3620,887],{"className":3621},[1077],[569,3623,3625],{"className":3624},[611],"6415",". Obwohl ",[569,3628,3630,3662],{"className":3629},[572],[569,3631,3633],{"className":3632},[576],[578,3634,3635],{"xmlns":580},[582,3636,3637,3659],{},[585,3638,3639,3641,3643,3645,3647,3649,3655,3657],{},[588,3640,868],{},[693,3642,760],{"stretchy":759},[588,3644,628],{},[693,3646,765],{"stretchy":759},[693,3648,877],{},[879,3650,3651,3653],{},[697,3652,699],{},[697,3654,3357],{},[693,3656,877],{},[697,3658,3416],{},[591,3660,3661],{"encoding":593},"E(X) = \\frac{1}{0{,}05} = 20",[569,3663,3665,3692,3785],{"className":3664,"ariaHidden":598},[597],[569,3666,3668,3671,3674,3677,3680,3683,3686,3689],{"className":3667},[602],[569,3669],{"className":3670,"style":778},[606],[569,3672,868],{"className":3673,"style":968},[611,612],[569,3675,760],{"className":3676},[785],[569,3678,628],{"className":3679,"style":644},[611,612],[569,3681,765],{"className":3682},[792],[569,3684],{"className":3685,"style":981},[719],[569,3687,877],{"className":3688},[985],[569,3690],{"className":3691,"style":981},[719],[569,3693,3695,3699,3776,3779,3782],{"className":3694},[602],[569,3696],{"className":3697,"style":3698},[606],"height:1.3262em;vertical-align:-0.4811em;",[569,3700,3702,3705,3773],{"className":3701},[611],[569,3703],{"className":3704},[785,1002],[569,3706,3708],{"className":3707},[879],[569,3709,3711,3765],{"className":3710},[1009,1010],[569,3712,3714,3762],{"className":3713},[1014],[569,3715,3717,3740,3748],{"className":3716,"style":2293},[1018],[569,3718,3719,3722],{"style":1973},[569,3720],{"className":3721,"style":1027},[1026],[569,3723,3725],{"className":3724},[1169,1170,1171,1172],[569,3726,3728,3731,3737],{"className":3727},[611,1172],[569,3729,1578],{"className":3730},[611,1172],[569,3732,3734],{"className":3733},[611,1172],[569,3735,887],{"className":3736},[1077,1172],[569,3738,3400],{"className":3739},[611,1172],[569,3741,3742,3745],{"style":1036},[569,3743],{"className":3744,"style":1027},[1026],[569,3746],{"className":3747,"style":1044},[1043],[569,3749,3750,3753],{"style":2318},[569,3751],{"className":3752,"style":1027},[1026],[569,3754,3756],{"className":3755},[1169,1170,1171,1172],[569,3757,3759],{"className":3758},[611,1172],[569,3760,699],{"className":3761},[611,1172],[569,3763,1061],{"className":3764},[1060],[569,3766,3768],{"className":3767},[1014],[569,3769,3771],{"className":3770,"style":2024},[1018],[569,3772],{},[569,3774],{"className":3775},[792,1002],[569,3777],{"className":3778,"style":981},[719],[569,3780,877],{"className":3781},[985],[569,3783],{"className":3784,"style":981},[719],[569,3786,3788,3791],{"className":3787},[602],[569,3789],{"className":3790,"style":734},[606],[569,3792,3416],{"className":3793},[611]," ist, liegt die Wahrscheinlichkeit also deutlich unter ",[569,3796,3798,3811],{"className":3797},[572],[569,3799,3801],{"className":3800},[576],[578,3802,3803],{"xmlns":580},[582,3804,3805,3809],{},[585,3806,3807],{},[697,3808,699],{},[591,3810,699],{"encoding":593},[569,3812,3814],{"className":3813,"ariaHidden":598},[597],[569,3815,3817,3820],{"className":3816},[602],[569,3818],{"className":3819,"style":734},[606],[569,3821,699],{"className":3822},[611],[560,3824,3826],{"id":3825},"typische-fehler","Typische Fehler",[3828,3829,3830,4023,4162,4165],"ul",{},[3831,3832,3833,3834,3862,3863,3913,3914,3942,3943,3993,3994,4022],"li",{},"Den Exponenten ",[569,3835,3837,3850],{"className":3836},[572],[569,3838,3840],{"className":3839},[576],[578,3841,3842],{"xmlns":580},[582,3843,3844,3848],{},[585,3845,3846],{},[588,3847,660],{},[591,3849,660],{"encoding":593},[569,3851,3853],{"className":3852,"ariaHidden":598},[597],[569,3854,3856,3859],{"className":3855},[602],[569,3857],{"className":3858,"style":672},[606],[569,3860,660],{"className":3861,"style":676},[611,612]," statt ",[569,3864,3866,3883],{"className":3865},[572],[569,3867,3869],{"className":3868},[576],[578,3870,3871],{"xmlns":580},[582,3872,3873,3881],{},[585,3874,3875,3877,3879],{},[588,3876,660],{},[693,3878,695],{},[697,3880,699],{},[591,3882,702],{"encoding":593},[569,3884,3886,3904],{"className":3885,"ariaHidden":598},[597],[569,3887,3889,3892,3895,3898,3901],{"className":3888},[602],[569,3890],{"className":3891,"style":712},[606],[569,3893,660],{"className":3894,"style":676},[611,612],[569,3896],{"className":3897,"style":720},[719],[569,3899,695],{"className":3900},[724],[569,3902],{"className":3903,"style":720},[719],[569,3905,3907,3910],{"className":3906},[602],[569,3908],{"className":3909,"style":734},[606],[569,3911,699],{"className":3912},[611]," nehmen. Vor dem Treffer im ",[569,3915,3917,3930],{"className":3916},[572],[569,3918,3920],{"className":3919},[576],[578,3921,3922],{"xmlns":580},[582,3923,3924,3928],{},[585,3925,3926],{},[588,3927,660],{},[591,3929,660],{"encoding":593},[569,3931,3933],{"className":3932,"ariaHidden":598},[597],[569,3934,3936,3939],{"className":3935},[602],[569,3937],{"className":3938,"style":672},[606],[569,3940,660],{"className":3941,"style":676},[611,612],"-ten Versuch liegen nur ",[569,3944,3946,3963],{"className":3945},[572],[569,3947,3949],{"className":3948},[576],[578,3950,3951],{"xmlns":580},[582,3952,3953,3961],{},[585,3954,3955,3957,3959],{},[588,3956,660],{},[693,3958,695],{},[697,3960,699],{},[591,3962,702],{"encoding":593},[569,3964,3966,3984],{"className":3965,"ariaHidden":598},[597],[569,3967,3969,3972,3975,3978,3981],{"className":3968},[602],[569,3970],{"className":3971,"style":712},[606],[569,3973,660],{"className":3974,"style":676},[611,612],[569,3976],{"className":3977,"style":720},[719],[569,3979,695],{"className":3980},[724],[569,3982],{"className":3983,"style":720},[719],[569,3985,3987,3990],{"className":3986},[602],[569,3988],{"className":3989,"style":734},[606],[569,3991,699],{"className":3992},[611]," Nieten. (Das passt nur zur anderen Konvention mit ",[569,3995,3997,4010],{"className":3996},[572],[569,3998,4000],{"className":3999},[576],[578,4001,4002],{"xmlns":580},[582,4003,4004,4008],{},[585,4005,4006],{},[588,4007,1561],{},[591,4009,1561],{"encoding":593},[569,4011,4013],{"className":4012,"ariaHidden":598},[597],[569,4014,4016,4019],{"className":4015},[602],[569,4017],{"className":4018,"style":640},[606],[569,4020,1561],{"className":4021,"style":720},[611,612],".)",[3831,4024,4025,4026,4161],{},"Die Konventionen mischen: ",[569,4027,4029,4057],{"className":4028},[572],[569,4030,4032],{"className":4031},[576],[578,4033,4034],{"xmlns":580},[582,4035,4036,4054],{},[585,4037,4038,4040,4042,4044,4046,4048],{},[588,4039,868],{},[693,4041,760],{"stretchy":759},[588,4043,628],{},[693,4045,765],{"stretchy":759},[693,4047,877],{},[879,4049,4050,4052],{},[697,4051,699],{},[588,4053,565],{},[591,4055,4056],{"encoding":593},"E(X) = \\frac{1}{p}",[569,4058,4060,4087],{"className":4059,"ariaHidden":598},[597],[569,4061,4063,4066,4069,4072,4075,4078,4081,4084],{"className":4062},[602],[569,4064],{"className":4065,"style":778},[606],[569,4067,868],{"className":4068,"style":968},[611,612],[569,4070,760],{"className":4071},[785],[569,4073,628],{"className":4074,"style":644},[611,612],[569,4076,765],{"className":4077},[792],[569,4079],{"className":4080,"style":981},[719],[569,4082,877],{"className":4083},[985],[569,4085],{"className":4086,"style":981},[719],[569,4088,4090,4093],{"className":4089},[602],[569,4091],{"className":4092,"style":3698},[606],[569,4094,4096,4099,4158],{"className":4095},[611],[569,4097],{"className":4098},[785,1002],[569,4100,4102],{"className":4101},[879],[569,4103,4105,4150],{"className":4104},[1009,1010],[569,4106,4108,4147],{"className":4107},[1014],[569,4109,4111,4125,4133],{"className":4110,"style":2293},[1018],[569,4112,4113,4116],{"style":1973},[569,4114],{"className":4115,"style":1027},[1026],[569,4117,4119],{"className":4118},[1169,1170,1171,1172],[569,4120,4122],{"className":4121},[611,1172],[569,4123,565],{"className":4124},[611,612,1172],[569,4126,4127,4130],{"style":1036},[569,4128],{"className":4129,"style":1027},[1026],[569,4131],{"className":4132,"style":1044},[1043],[569,4134,4135,4138],{"style":2318},[569,4136],{"className":4137,"style":1027},[1026],[569,4139,4141],{"className":4140},[1169,1170,1171,1172],[569,4142,4144],{"className":4143},[611,1172],[569,4145,699],{"className":4146},[611,1172],[569,4148,1061],{"className":4149},[1060],[569,4151,4153],{"className":4152},[1014],[569,4154,4156],{"className":4155,"style":2024},[1018],[569,4157],{},[569,4159],{"className":4160},[792,1002]," gilt für die Versuchsnummer, nicht für die Anzahl der Nieten.",[3831,4163,4164],{},"Annehmen, nach vielen Nieten sei ein Treffer „überfällig“. Wegen der Gedächtnislosigkeit ändert sich die Wahrscheinlichkeit nicht.",[3831,4166,4167,4168,4212,4213,4311,4312,4340,4341,4499,4500,2213],{},"Mit ",[569,4169,4171,4191],{"className":4170},[572],[569,4172,4174],{"className":4173},[576],[578,4175,4176],{"xmlns":580},[582,4177,4178,4188],{},[585,4179,4180,4182,4184,4186],{},[588,4181,868],{},[693,4183,760],{"stretchy":759},[588,4185,628],{},[693,4187,765],{"stretchy":759},[591,4189,4190],{"encoding":593},"E(X)",[569,4192,4194],{"className":4193,"ariaHidden":598},[597],[569,4195,4197,4200,4203,4206,4209],{"className":4196},[602],[569,4198],{"className":4199,"style":778},[606],[569,4201,868],{"className":4202,"style":968},[611,612],[569,4204,760],{"className":4205},[785],[569,4207,628],{"className":4208,"style":644},[611,612],[569,4210,765],{"className":4211},[792]," Versuchen einen sicheren Treffer erwarten. Nach ",[569,4214,4216,4234],{"className":4215},[572],[569,4217,4219],{"className":4218},[576],[578,4220,4221],{"xmlns":580},[582,4222,4223,4231],{},[585,4224,4225],{},[879,4226,4227,4229],{},[697,4228,699],{},[588,4230,565],{},[591,4232,4233],{"encoding":593},"\\frac{1}{p}",[569,4235,4237],{"className":4236,"ariaHidden":598},[597],[569,4238,4240,4243],{"className":4239},[602],[569,4241],{"className":4242,"style":3698},[606],[569,4244,4246,4249,4308],{"className":4245},[611],[569,4247],{"className":4248},[785,1002],[569,4250,4252],{"className":4251},[879],[569,4253,4255,4300],{"className":4254},[1009,1010],[569,4256,4258,4297],{"className":4257},[1014],[569,4259,4261,4275,4283],{"className":4260,"style":2293},[1018],[569,4262,4263,4266],{"style":1973},[569,4264],{"className":4265,"style":1027},[1026],[569,4267,4269],{"className":4268},[1169,1170,1171,1172],[569,4270,4272],{"className":4271},[611,1172],[569,4273,565],{"className":4274},[611,612,1172],[569,4276,4277,4280],{"style":1036},[569,4278],{"className":4279,"style":1027},[1026],[569,4281],{"className":4282,"style":1044},[1043],[569,4284,4285,4288],{"style":2318},[569,4286],{"className":4287,"style":1027},[1026],[569,4289,4291],{"className":4290},[1169,1170,1171,1172],[569,4292,4294],{"className":4293},[611,1172],[569,4295,699],{"className":4296},[611,1172],[569,4298,1061],{"className":4299},[1060],[569,4301,4303],{"className":4302},[1014],[569,4304,4306],{"className":4305,"style":2024},[1018],[569,4307],{},[569,4309],{"className":4310},[792,1002]," Versuchen ist der erste Treffer bei kleinem ",[569,4313,4315,4328],{"className":4314},[572],[569,4316,4318],{"className":4317},[576],[578,4319,4320],{"xmlns":580},[582,4321,4322,4326],{},[585,4323,4324],{},[588,4325,565],{},[591,4327,565],{"encoding":593},[569,4329,4331],{"className":4330,"ariaHidden":598},[597],[569,4332,4334,4337],{"className":4333},[602],[569,4335],{"className":4336,"style":607},[606],[569,4338,565],{"className":4339},[611,612]," nur mit etwa ",[569,4342,4344,4379],{"className":4343},[572],[569,4345,4347],{"className":4346},[576],[578,4348,4349],{"xmlns":580},[582,4350,4351,4376],{},[585,4352,4353,4355,4357,4364,4366,4369,4373],{},[697,4354,699],{},[693,4356,695],{},[879,4358,4359,4361],{},[697,4360,699],{},[588,4362,4363],{},"e",[693,4365,2414],{},[697,4367,4368],{},"63",[4370,4371,4372],"mtext",{}," ",[588,4374,4375],{"mathvariant":808},"%",[591,4377,4378],{"encoding":593},"1 - \\frac{1}{e} \\approx 63\\,\\%",[569,4380,4382,4400,4483],{"className":4381,"ariaHidden":598},[597],[569,4383,4385,4388,4391,4394,4397],{"className":4384},[602],[569,4386],{"className":4387,"style":3532},[606],[569,4389,699],{"className":4390},[611],[569,4392],{"className":4393,"style":720},[719],[569,4395,695],{"className":4396},[724],[569,4398],{"className":4399,"style":720},[719],[569,4401,4403,4406,4474,4477,4480],{"className":4402},[602],[569,4404],{"className":4405,"style":2274},[606],[569,4407,4409,4412,4471],{"className":4408},[611],[569,4410],{"className":4411},[785,1002],[569,4413,4415],{"className":4414},[879],[569,4416,4418,4463],{"className":4417},[1009,1010],[569,4419,4421,4460],{"className":4420},[1014],[569,4422,4424,4438,4446],{"className":4423,"style":2293},[1018],[569,4425,4426,4429],{"style":1973},[569,4427],{"className":4428,"style":1027},[1026],[569,4430,4432],{"className":4431},[1169,1170,1171,1172],[569,4433,4435],{"className":4434},[611,1172],[569,4436,4363],{"className":4437},[611,612,1172],[569,4439,4440,4443],{"style":1036},[569,4441],{"className":4442,"style":1027},[1026],[569,4444],{"className":4445,"style":1044},[1043],[569,4447,4448,4451],{"style":2318},[569,4449],{"className":4450,"style":1027},[1026],[569,4452,4454],{"className":4453},[1169,1170,1171,1172],[569,4455,4457],{"className":4456},[611,1172],[569,4458,699],{"className":4459},[611,1172],[569,4461,1061],{"className":4462},[1060],[569,4464,4466],{"className":4465},[1014],[569,4467,4469],{"className":4468,"style":2340},[1018],[569,4470],{},[569,4472],{"className":4473},[792,1002],[569,4475],{"className":4476,"style":981},[719],[569,4478,2414],{"className":4479},[985],[569,4481],{"className":4482,"style":981},[719],[569,4484,4486,4490,4493,4496],{"className":4485},[602],[569,4487],{"className":4488,"style":4489},[606],"height:0.8056em;vertical-align:-0.0556em;",[569,4491,4368],{"className":4492},[611],[569,4494],{"className":4495,"style":1085},[719],[569,4497,4375],{"className":4498},[611]," eingetreten, im Losbeispiel mit ",[569,4501,4503,4522],{"className":4502},[572],[569,4504,4506],{"className":4505},[576],[578,4507,4508],{"xmlns":580},[582,4509,4510,4519],{},[585,4511,4512,4515,4517],{},[697,4513,4514],{},"64",[4370,4516,4372],{},[588,4518,4375],{"mathvariant":808},[591,4520,4521],{"encoding":593},"64\\,\\%",[569,4523,4525],{"className":4524,"ariaHidden":598},[597],[569,4526,4528,4531,4534,4537],{"className":4527},[602],[569,4529],{"className":4530,"style":4489},[606],[569,4532,4514],{"className":4533},[611],[569,4535],{"className":4536,"style":1085},[719],[569,4538,4375],{"className":4539},[611],{"title":4541,"searchDepth":4542,"depth":4542,"links":4543},"",2,[4544,4545,4546],{"id":562,"depth":4542,"text":563},{"id":2216,"depth":4542,"text":2217},{"id":3825,"depth":4542,"text":3826},[4548,4551,4554,4557,4560,4562,4564,4567,4570,4572],{"lhs":4549,"rhs":4550},"p + (1-p)*p + (1-p)^2*p","1 - (1-p)^3",{"lhs":4552,"rhs":4553},"(5\u002F6)^2 * 1\u002F6","25\u002F216",{"lhs":4555,"rhs":4556},"round(25\u002F216, 4)","0.1157",{"lhs":4558,"rhs":4559},"1\u002Fp - 1","(1-p)\u002Fp",{"lhs":4561,"rhs":2243},"1 \u002F (1\u002F6)",{"lhs":4563,"rhs":2982},"(1 - 1\u002F6) \u002F (1\u002F6)^2",{"lhs":4565,"rhs":4566},"round((5\u002F6)^10, 4)","0.1615",{"lhs":4568,"rhs":4569},"round(1 - 0.95^20, 4)","0.6415",{"lhs":4571,"rhs":3416},"1 \u002F 0.05",{"lhs":4573,"rhs":4368},"round((1 - exp(-1)) * 100)","0 \u003C p \\leq 1,\\ k \\in \\{1, 2, 3, \\ldots\\}","\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>p\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 < p \\leq 1,\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:0.6835em;vertical-align:-0.0391em;\">\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:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo stretchy=\"false\">}\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\{1, 2, 3, \\ldots\\}\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\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mclose\">}\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","geometric-distribution","P(X = k) = (1-p)^{k-1} \\cdot p","\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>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X = k) = (1-p)^{k-1} \\cdot p\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\" 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class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1491em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\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>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgeometrische-verteilung",[],[4587,4588,4589,4590],"binomial-distribution","exponential-distribution","path-multiplication-rule","expected-value",{"title":548,"description":4541},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgeometrische-verteilung","Wahrscheinlichkeit, dass der erste Treffer einer Bernoulli-Kette genau im k-ten Versuch eintritt.",[4595,4596,4597,4598,4599],"wartezeit","erster treffer","diskrete 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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>",{"symbol":565,"meaning":4608,"symbolHtml":4609},"Trefferwahrscheinlichkeit bei jedem Versuch","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","gUQysoJcjMswFeZ22AxTzCsWG3J93M4Z4SrbGaL_7Ss",[4612,4615,4618,4621],{"stem":4613,"title":4614,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":4616,"title":4617,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert","Erwartungswert",{"stem":4619,"title":4620,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fexponentialverteilung","Exponentialverteilung",{"stem":4622,"title":4623,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel","Pfadmultiplikationsregel",1793824285658]