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P_{\\min}",[568,907,909,928,949,1000,1084,1105,1152,1170],{"className":908,"ariaHidden":608},[607],[568,910,912,916,919,922,925],{"className":911},[612],[568,913],{"className":914,"style":915},[616],"height:0.7278em;vertical-align:-0.0833em;",[568,917,719],{"className":918},[621],[568,920],{"className":921,"style":756},[625],[568,923,722],{"className":924},[760],[568,926],{"className":927,"style":756},[625],[568,929,931,934,937,940,943,946],{"className":930},[612],[568,932],{"className":933,"style":745},[616],[568,935,716],{"className":936},[749],[568,938,719],{"className":939},[621],[568,941],{"className":942,"style":756},[625],[568,944,722],{"className":945},[760],[568,947],{"className":948,"style":756},[625],[568,950,952,955,958,989,993,997],{"className":951},[612],[568,953],{"className":954,"style":745},[616],[568,956,564],{"className":957},[621,661],[568,959,961,964],{"className":960},[776],[568,962,730],{"className":963},[776],[568,965,967],{"className":966},[783],[568,968,970],{"className":969},[787],[568,971,973],{"className":972},[791],[568,974,977],{"className":975,"style":976},[795],"height:0.7144em;",[568,978,980,983],{"style":979},"top:-3.113em;margin-right:0.05em;",[568,981],{"className":982,"style":804},[803],[568,984,986],{"className":985},[808,809,810,811],[568,987,645],{"className":988},[621,661,811],[568,990],{"className":991,"style":992},[625],"margin-right:0.2778em;",[568,994,853],{"className":995},[996],"mrel",[568,998],{"className":999,"style":992},[625],[568,1001,1003,1007,1069,1072,1075,1078,1081],{"className":1002},[612],[568,1004],{"className":1005,"style":1006},[616],"height:0.8333em;vertical-align:-0.15em;",[568,1008,1010,1014],{"className":1009},[621],[568,1011,859],{"className":1012,"style":1013},[621,661],"margin-right:0.1389em;",[568,1015,1017],{"className":1016},[783],[568,1018,1021,1060],{"className":1019},[787,1020],"vlist-t2",[568,1022,1024,1055],{"className":1023},[791],[568,1025,1028],{"className":1026,"style":1027},[795],"height:0.3175em;",[568,1029,1031,1034],{"style":1030},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[568,1032],{"className":1033,"style":804},[803],[568,1035,1037],{"className":1036},[808,809,810,811],[568,1038,1040],{"className":1039},[621,811],[568,1041,1044,1048,1052],{"className":1042},[1043,811],"mop",[568,1045,1047],{"className":1046},[811],"m",[568,1049,1051],{"className":1050},[811],"i",[568,1053,645],{"className":1054},[811],[568,1056,1059],{"className":1057},[1058],"vlist-s","​",[568,1061,1063],{"className":1062},[791],[568,1064,1067],{"className":1065,"style":1066},[795],"height:0.15em;",[568,1068],{},[568,1070],{"className":1071,"style":992},[625],[568,1073],{"className":1074,"style":992},[625],[568,1076,871],{"className":1077},[996],[568,1079],{"className":1080,"style":992},[625],[568,1082],{"className":1083,"style":992},[625],[568,1085,1087,1090,1093,1096,1099,1102],{"className":1086},[612],[568,1088],{"className":1089,"style":745},[616],[568,1091,716],{"className":1092},[749],[568,1094,719],{"className":1095},[621],[568,1097],{"className":1098,"style":756},[625],[568,1100,722],{"className":1101},[760],[568,1103],{"className":1104,"style":756},[625],[568,1106,1108,1111,1114,1143,1146,1149],{"className":1107},[612],[568,1109],{"className":1110,"style":745},[616],[568,1112,564],{"className":1113},[621,661],[568,1115,1117,1120],{"className":1116},[776],[568,1118,730],{"className":1119},[776],[568,1121,1123],{"className":1122},[783],[568,1124,1126],{"className":1125},[787],[568,1127,1129],{"className":1128},[791],[568,1130,1132],{"className":1131,"style":976},[795],[568,1133,1134,1137],{"style":979},[568,1135],{"className":1136,"style":804},[803],[568,1138,1140],{"className":1139},[808,809,810,811],[568,1141,645],{"className":1142},[621,661,811],[568,1144],{"className":1145,"style":992},[625],[568,1147,890],{"className":1148},[996],[568,1150],{"className":1151,"style":992},[625],[568,1153,1155,1158,1161,1164,1167],{"className":1154},[612],[568,1156],{"className":1157,"style":915},[616],[568,1159,719],{"className":1160},[621],[568,1162],{"className":1163,"style":756},[625],[568,1165,722],{"className":1166},[760],[568,1168],{"className":1169,"style":756},[625],[568,1171,1173,1176],{"className":1172},[612],[568,1174],{"className":1175,"style":1006},[616],[568,1177,1179,1182],{"className":1178},[621],[568,1180,859],{"className":1181,"style":1013},[621,661],[568,1183,1185],{"className":1184},[783],[568,1186,1188,1220],{"className":1187},[787,1020],[568,1189,1191,1217],{"className":1190},[791],[568,1192,1194],{"className":1193,"style":1027},[795],[568,1195,1196,1199],{"style":1030},[568,1197],{"className":1198,"style":804},[803],[568,1200,1202],{"className":1201},[808,809,810,811],[568,1203,1205],{"className":1204},[621,811],[568,1206,1208,1211,1214],{"className":1207},[1043,811],[568,1209,1047],{"className":1210},[811],[568,1212,1051],{"className":1213},[811],[568,1215,645],{"className":1216},[811],[568,1218,1059],{"className":1219},[1058],[568,1221,1223],{"className":1222},[791],[568,1224,1226],{"className":1225,"style":1066},[795],[568,1227],{},[564,1229,1230,1231,1300,1301,1401,1402,1405,1406,1409],{},"Nun logarithmiert man beide Seiten und teilt durch ",[568,1232,1234,1261],{"className":1233},[571],[568,1235,1237],{"className":1236},[575],[577,1238,1239],{"xmlns":579},[581,1240,1241,1258],{},[584,1242,1243,1246,1248,1250,1252,1254,1256],{},[595,1244,1245],{},"ln",[713,1247,865],{},[713,1249,716],{"stretchy":715},[587,1251,719],{},[713,1253,722],{},[595,1255,564],{},[713,1257,730],{"stretchy":715},[600,1259,1260],{"encoding":602},"\\ln(1-p)",[568,1262,1264,1288],{"className":1263,"ariaHidden":608},[607],[568,1265,1267,1270,1273,1276,1279,1282,1285],{"className":1266},[612],[568,1268],{"className":1269,"style":745},[616],[568,1271,1245],{"className":1272},[1043],[568,1274,716],{"className":1275},[749],[568,1277,719],{"className":1278},[621],[568,1280],{"className":1281,"style":756},[625],[568,1283,722],{"className":1284},[760],[568,1286],{"className":1287,"style":756},[625],[568,1289,1291,1294,1297],{"className":1290},[612],[568,1292],{"className":1293,"style":745},[616],[568,1295,564],{"className":1296},[621,661],[568,1298,730],{"className":1299},[776],". Weil ",[568,1302,1304,1332],{"className":1303},[571],[568,1305,1307],{"className":1306},[575],[577,1308,1309],{"xmlns":579},[581,1310,1311,1329],{},[584,1312,1313,1316,1319,1321,1323,1325,1327],{},[587,1314,1315],{},"0",[713,1317,1318],{},"\u003C",[587,1320,719],{},[713,1322,722],{},[595,1324,564],{},[713,1326,1318],{},[587,1328,719],{},[600,1330,1331],{"encoding":602},"0 \u003C 1-p \u003C 1",[568,1333,1335,1354,1372,1391],{"className":1334,"ariaHidden":608},[607],[568,1336,1338,1342,1345,1348,1351],{"className":1337},[612],[568,1339],{"className":1340,"style":1341},[616],"height:0.6835em;vertical-align:-0.0391em;",[568,1343,1315],{"className":1344},[621],[568,1346],{"className":1347,"style":992},[625],[568,1349,1318],{"className":1350},[996],[568,1352],{"className":1353,"style":992},[625],[568,1355,1357,1360,1363,1366,1369],{"className":1356},[612],[568,1358],{"className":1359,"style":915},[616],[568,1361,719],{"className":1362},[621],[568,1364],{"className":1365,"style":756},[625],[568,1367,722],{"className":1368},[760],[568,1370],{"className":1371,"style":756},[625],[568,1373,1375,1379,1382,1385,1388],{"className":1374},[612],[568,1376],{"className":1377,"style":1378},[616],"height:0.7335em;vertical-align:-0.1944em;",[568,1380,564],{"className":1381},[621,661],[568,1383],{"className":1384,"style":992},[625],[568,1386,1318],{"className":1387},[996],[568,1389],{"className":1390,"style":992},[625],[568,1392,1394,1398],{"className":1393},[612],[568,1395],{"className":1396,"style":1397},[616],"height:0.6444em;",[568,1399,719],{"className":1400},[621]," ist, ist dieser Logarithmus ",[667,1403,1404],{},"negativ",", und das Ungleichheitszeichen dreht sich um. Das Ergebnis rundet man immer ",[667,1407,1408],{},"auf"," die nächste ganze Zahl.",[564,1411,1412],{},"Die Versuche müssen unabhängig sein und dieselbe Trefferwahrscheinlichkeit haben (Bernoulli-Kette).",[559,1414,1416],{"id":1415},"beispiele","Beispiele",[564,1418,1419,1420,1458,1459,1593,1594,1714],{},"Mindestens eine Sechs mit mindestens ",[568,1421,1423,1440],{"className":1422},[571],[568,1424,1426],{"className":1425},[575],[577,1427,1428],{"xmlns":579},[581,1429,1430,1438],{},[584,1431,1432,1434,1436],{},[587,1433,589],{},[591,1435,593],{},[595,1437,598],{"mathvariant":597},[600,1439,603],{"encoding":602},[568,1441,1443],{"className":1442,"ariaHidden":608},[607],[568,1444,1446,1449,1452,1455],{"className":1445},[612],[568,1447],{"className":1448,"style":617},[616],[568,1450,589],{"className":1451},[621],[568,1453],{"className":1454,"style":626},[625],[568,1456,598],{"className":1457},[621],", also ",[568,1460,1462,1487],{"className":1461},[571],[568,1463,1465],{"className":1464},[575],[577,1466,1467],{"xmlns":579},[581,1468,1469,1484],{},[584,1470,1471,1473,1476],{},[595,1472,564],{},[713,1474,1475],{},"=",[1477,1478,1479,1481],"mfrac",{},[587,1480,719],{},[587,1482,1483],{},"6",[600,1485,1486],{"encoding":602},"p = \\frac{1}{6}",[568,1488,1490,1509],{"className":1489,"ariaHidden":608},[607],[568,1491,1493,1497,1500,1503,1506],{"className":1492},[612],[568,1494],{"className":1495,"style":1496},[616],"height:0.625em;vertical-align:-0.1944em;",[568,1498,564],{"className":1499},[621,661],[568,1501],{"className":1502,"style":992},[625],[568,1504,1475],{"className":1505},[996],[568,1507],{"className":1508,"style":992},[625],[568,1510,1512,1516],{"className":1511},[612],[568,1513],{"className":1514,"style":1515},[616],"height:1.1901em;vertical-align:-0.345em;",[568,1517,1519,1523,1590],{"className":1518},[621],[568,1520],{"className":1521},[749,1522],"nulldelimiter",[568,1524,1526],{"className":1525},[1477],[568,1527,1529,1581],{"className":1528},[787,1020],[568,1530,1532,1578],{"className":1531},[791],[568,1533,1536,1552,1563],{"className":1534,"style":1535},[795],"height:0.8451em;",[568,1537,1539,1543],{"style":1538},"top:-2.655em;",[568,1540],{"className":1541,"style":1542},[803],"height:3em;",[568,1544,1546],{"className":1545},[808,809,810,811],[568,1547,1549],{"className":1548},[621,811],[568,1550,1483],{"className":1551},[621,811],[568,1553,1555,1558],{"style":1554},"top:-3.23em;",[568,1556],{"className":1557,"style":1542},[803],[568,1559],{"className":1560,"style":1562},[1561],"frac-line","border-bottom-width:0.04em;",[568,1564,1566,1569],{"style":1565},"top:-3.394em;",[568,1567],{"className":1568,"style":1542},[803],[568,1570,1572],{"className":1571},[808,809,810,811],[568,1573,1575],{"className":1574},[621,811],[568,1576,719],{"className":1577},[621,811],[568,1579,1059],{"className":1580},[1058],[568,1582,1584],{"className":1583},[791],[568,1585,1588],{"className":1586,"style":1587},[795],"height:0.345em;",[568,1589],{},[568,1591],{"className":1592},[776,1522]," und ",[568,1595,1597,1622],{"className":1596},[571],[568,1598,1600],{"className":1599},[575],[577,1601,1602],{"xmlns":579},[581,1603,1604,1619],{},[584,1605,1606,1614,1616],{},[855,1607,1608,1610,1612],{},[595,1609,859],{},[595,1611,862],{},[713,1613,865],{},[713,1615,1475],{},[587,1617,1618],{},"0,9",[600,1620,1621],{"encoding":602},"P_{\\min} = 0{,}9",[568,1623,1625,1692],{"className":1624,"ariaHidden":608},[607],[568,1626,1628,1631,1683,1686,1689],{"className":1627},[612],[568,1629],{"className":1630,"style":1006},[616],[568,1632,1634,1637],{"className":1633},[621],[568,1635,859],{"className":1636,"style":1013},[621,661],[568,1638,1640],{"className":1639},[783],[568,1641,1643,1675],{"className":1642},[787,1020],[568,1644,1646,1672],{"className":1645},[791],[568,1647,1649],{"className":1648,"style":1027},[795],[568,1650,1651,1654],{"style":1030},[568,1652],{"className":1653,"style":804},[803],[568,1655,1657],{"className":1656},[808,809,810,811],[568,1658,1660],{"className":1659},[621,811],[568,1661,1663,1666,1669],{"className":1662},[1043,811],[568,1664,1047],{"className":1665},[811],[568,1667,1051],{"className":1668},[811],[568,1670,645],{"className":1671},[811],[568,1673,1059],{"className":1674},[1058],[568,1676,1678],{"className":1677},[791],[568,1679,1681],{"className":1680,"style":1066},[795],[568,1682],{},[568,1684],{"className":1685,"style":992},[625],[568,1687,1475],{"className":1688},[996],[568,1690],{"className":1691,"style":992},[625],[568,1693,1695,1699,1702,1710],{"className":1694},[612],[568,1696],{"className":1697,"style":1698},[616],"height:0.8389em;vertical-align:-0.1944em;",[568,1700,1315],{"className":1701},[621],[568,1703,1705],{"className":1704},[621],[568,1706,1709],{"className":1707},[1708],"mpunct",",",[568,1711,1713],{"className":1712},[621],"9",":",[568,1716,1718],{"className":1717},[819],[568,1719,1721,1777],{"className":1720},[571],[568,1722,1724],{"className":1723},[575],[577,1725,1726],{"xmlns":579,"display":828},[581,1727,1728,1774],{},[584,1729,1730,1732,1734,1768,1771],{},[595,1731,645],{},[713,1733,853],{},[1477,1735,1736,1749],{},[584,1737,1738,1740,1742,1744,1747],{},[595,1739,1245],{},[713,1741,865],{},[713,1743,716],{"stretchy":715},[587,1745,1746],{},"0,1",[713,1748,730],{"stretchy":715},[584,1750,1751,1753,1755],{},[595,1752,1245],{},[713,1754,865],{},[584,1756,1757,1759,1766],{},[713,1758,716],{"fence":608},[1477,1760,1761,1764],{},[587,1762,1763],{},"5",[587,1765,1483],{},[713,1767,730],{"fence":608},[713,1769,1770],{},"≈",[587,1772,1773],{},"12,63",[600,1775,1776],{"encoding":602},"n \\geq \\frac{\\ln(0{,}1)}{\\ln\\left(\\frac{5}{6}\\right)} \\approx 12{,}63",[568,1778,1780,1799,1990],{"className":1779,"ariaHidden":608},[607],[568,1781,1783,1787,1790,1793,1796],{"className":1782},[612],[568,1784],{"className":1785,"style":1786},[616],"height:0.7719em;vertical-align:-0.136em;",[568,1788,645],{"className":1789},[621,661],[568,1791],{"className":1792,"style":992},[625],[568,1794,853],{"className":1795},[996],[568,1797],{"className":1798,"style":992},[625],[568,1800,1802,1806,1981,1984,1987],{"className":1801},[612],[568,1803],{"className":1804,"style":1805},[616],"height:2.517em;vertical-align:-1.09em;",[568,1807,1809,1812,1978],{"className":1808},[621],[568,1810],{"className":1811},[749,1522],[568,1813,1815],{"className":1814},[1477],[568,1816,1818,1969],{"className":1817},[787,1020],[568,1819,1821,1966],{"className":1820},[791],[568,1822,1825,1928,1936],{"className":1823,"style":1824},[795],"height:1.427em;",[568,1826,1828,1831],{"style":1827},"top:-2.26em;",[568,1829],{"className":1830,"style":1542},[803],[568,1832,1834,1837,1840],{"className":1833},[621],[568,1835,1245],{"className":1836},[1043],[568,1838],{"className":1839,"style":626},[625],[568,1841,1844,1854,1922],{"className":1842},[1843],"minner",[568,1845,1849],{"className":1846,"style":1848},[749,1847],"delimcenter","top:0em;",[568,1850,716],{"className":1851},[1852,1853],"delimsizing","size1",[568,1855,1857,1860,1919],{"className":1856},[621],[568,1858],{"className":1859},[749,1522],[568,1861,1863],{"className":1862},[1477],[568,1864,1866,1911],{"className":1865},[787,1020],[568,1867,1869,1908],{"className":1868},[791],[568,1870,1872,1886,1894],{"className":1871,"style":1535},[795],[568,1873,1874,1877],{"style":1538},[568,1875],{"className":1876,"style":1542},[803],[568,1878,1880],{"className":1879},[808,809,810,811],[568,1881,1883],{"className":1882},[621,811],[568,1884,1483],{"className":1885},[621,811],[568,1887,1888,1891],{"style":1554},[568,1889],{"className":1890,"style":1542},[803],[568,1892],{"className":1893,"style":1562},[1561],[568,1895,1896,1899],{"style":1565},[568,1897],{"className":1898,"style":1542},[803],[568,1900,1902],{"className":1901},[808,809,810,811],[568,1903,1905],{"className":1904},[621,811],[568,1906,1763],{"className":1907},[621,811],[568,1909,1059],{"className":1910},[1058],[568,1912,1914],{"className":1913},[791],[568,1915,1917],{"className":1916,"style":1587},[795],[568,1918],{},[568,1920],{"className":1921},[776,1522],[568,1923,1925],{"className":1924,"style":1848},[776,1847],[568,1926,730],{"className":1927},[1852,1853],[568,1929,1930,1933],{"style":1554},[568,1931],{"className":1932,"style":1542},[803],[568,1934],{"className":1935,"style":1562},[1561],[568,1937,1939,1942],{"style":1938},"top:-3.677em;",[568,1940],{"className":1941,"style":1542},[803],[568,1943,1945,1948,1951,1954,1960,1963],{"className":1944},[621],[568,1946,1245],{"className":1947},[1043],[568,1949,716],{"className":1950},[749],[568,1952,1315],{"className":1953},[621],[568,1955,1957],{"className":1956},[621],[568,1958,1709],{"className":1959},[1708],[568,1961,719],{"className":1962},[621],[568,1964,730],{"className":1965},[776],[568,1967,1059],{"className":1968},[1058],[568,1970,1972],{"className":1971},[791],[568,1973,1976],{"className":1974,"style":1975},[795],"height:1.09em;",[568,1977],{},[568,1979],{"className":1980},[776,1522],[568,1982],{"className":1983,"style":992},[625],[568,1985,1770],{"className":1986},[996],[568,1988],{"className":1989,"style":992},[625],[568,1991,1993,1996,2000,2006],{"className":1992},[612],[568,1994],{"className":1995,"style":1698},[616],[568,1997,1999],{"className":1998},[621],"12",[568,2001,2003],{"className":2002},[621],[568,2004,1709],{"className":2005},[1708],[568,2007,2009],{"className":2008},[621],"63",[564,2011,2012,2013,2042,2043,2253,2254,2461],{},"Man muss also mindestens ",[568,2014,2016,2030],{"className":2015},[571],[568,2017,2019],{"className":2018},[575],[577,2020,2021],{"xmlns":579},[581,2022,2023,2028],{},[584,2024,2025],{},[587,2026,2027],{},"13",[600,2029,2027],{"encoding":602},[568,2031,2033],{"className":2032,"ariaHidden":608},[607],[568,2034,2036,2039],{"className":2035},[612],[568,2037],{"className":2038,"style":1397},[616],[568,2040,2027],{"className":2041},[621],"-mal würfeln. Probe: ",[568,2044,2046,2083],{"className":2045},[571],[568,2047,2049],{"className":2048},[575],[577,2050,2051],{"xmlns":579},[581,2052,2053,2080],{},[584,2054,2055,2057,2059,2075,2077],{},[587,2056,719],{},[713,2058,722],{},[726,2060,2061,2073],{},[584,2062,2063,2065,2071],{},[713,2064,716],{"fence":608},[1477,2066,2067,2069],{},[587,2068,1763],{},[587,2070,1483],{},[713,2072,730],{"fence":608},[587,2074,2027],{},[713,2076,1770],{},[587,2078,2079],{},"0,9065",[600,2081,2082],{"encoding":602},"1 - \\left(\\frac{5}{6}\\right)^{13} \\approx 0{,}9065",[568,2084,2086,2104,2234],{"className":2085,"ariaHidden":608},[607],[568,2087,2089,2092,2095,2098,2101],{"className":2088},[612],[568,2090],{"className":2091,"style":915},[616],[568,2093,719],{"className":2094},[621],[568,2096],{"className":2097,"style":756},[625],[568,2099,722],{"className":2100},[760],[568,2102],{"className":2103,"style":756},[625],[568,2105,2107,2111,2225,2228,2231],{"className":2106},[612],[568,2108],{"className":2109,"style":2110},[616],"height:1.404em;vertical-align:-0.35em;",[568,2112,2114,2197],{"className":2113},[1843],[568,2115,2117,2123,2191],{"className":2116},[1843],[568,2118,2120],{"className":2119,"style":1848},[749,1847],[568,2121,716],{"className":2122},[1852,1853],[568,2124,2126,2129,2188],{"className":2125},[621],[568,2127],{"className":2128},[749,1522],[568,2130,2132],{"className":2131},[1477],[568,2133,2135,2180],{"className":2134},[787,1020],[568,2136,2138,2177],{"className":2137},[791],[568,2139,2141,2155,2163],{"className":2140,"style":1535},[795],[568,2142,2143,2146],{"style":1538},[568,2144],{"className":2145,"style":1542},[803],[568,2147,2149],{"className":2148},[808,809,810,811],[568,2150,2152],{"className":2151},[621,811],[568,2153,1483],{"className":2154},[621,811],[568,2156,2157,2160],{"style":1554},[568,2158],{"className":2159,"style":1542},[803],[568,2161],{"className":2162,"style":1562},[1561],[568,2164,2165,2168],{"style":1565},[568,2166],{"className":2167,"style":1542},[803],[568,2169,2171],{"className":2170},[808,809,810,811],[568,2172,2174],{"className":2173},[621,811],[568,2175,1763],{"className":2176},[621,811],[568,2178,1059],{"className":2179},[1058],[568,2181,2183],{"className":2182},[791],[568,2184,2186],{"className":2185,"style":1587},[795],[568,2187],{},[568,2189],{"className":2190},[776,1522],[568,2192,2194],{"className":2193,"style":1848},[776,1847],[568,2195,730],{"className":2196},[1852,1853],[568,2198,2200],{"className":2199},[783],[568,2201,2203],{"className":2202},[787],[568,2204,2206],{"className":2205},[791],[568,2207,2210],{"className":2208,"style":2209},[795],"height:1.054em;",[568,2211,2213,2216],{"style":2212},"top:-3.3029em;margin-right:0.05em;",[568,2214],{"className":2215,"style":804},[803],[568,2217,2219],{"className":2218},[808,809,810,811],[568,2220,2222],{"className":2221},[621,811],[568,2223,2027],{"className":2224},[621,811],[568,2226],{"className":2227,"style":992},[625],[568,2229,1770],{"className":2230},[996],[568,2232],{"className":2233,"style":992},[625],[568,2235,2237,2240,2243,2249],{"className":2236},[612],[568,2238],{"className":2239,"style":1698},[616],[568,2241,1315],{"className":2242},[621],[568,2244,2246],{"className":2245},[621],[568,2247,1709],{"className":2248},[1708],[568,2250,2252],{"className":2251},[621],"9065",", aber ",[568,2255,2257,2294],{"className":2256},[571],[568,2258,2260],{"className":2259},[575],[577,2261,2262],{"xmlns":579},[581,2263,2264,2291],{},[584,2265,2266,2268,2270,2286,2288],{},[587,2267,719],{},[713,2269,722],{},[726,2271,2272,2284],{},[584,2273,2274,2276,2282],{},[713,2275,716],{"fence":608},[1477,2277,2278,2280],{},[587,2279,1763],{},[587,2281,1483],{},[713,2283,730],{"fence":608},[587,2285,1999],{},[713,2287,1770],{},[587,2289,2290],{},"0,8878",[600,2292,2293],{"encoding":602},"1 - \\left(\\frac{5}{6}\\right)^{12} \\approx 0{,}8878",[568,2295,2297,2315,2442],{"className":2296,"ariaHidden":608},[607],[568,2298,2300,2303,2306,2309,2312],{"className":2299},[612],[568,2301],{"className":2302,"style":915},[616],[568,2304,719],{"className":2305},[621],[568,2307],{"className":2308,"style":756},[625],[568,2310,722],{"className":2311},[760],[568,2313],{"className":2314,"style":756},[625],[568,2316,2318,2321,2433,2436,2439],{"className":2317},[612],[568,2319],{"className":2320,"style":2110},[616],[568,2322,2324,2407],{"className":2323},[1843],[568,2325,2327,2333,2401],{"className":2326},[1843],[568,2328,2330],{"className":2329,"style":1848},[749,1847],[568,2331,716],{"className":2332},[1852,1853],[568,2334,2336,2339,2398],{"className":2335},[621],[568,2337],{"className":2338},[749,1522],[568,2340,2342],{"className":2341},[1477],[568,2343,2345,2390],{"className":2344},[787,1020],[568,2346,2348,2387],{"className":2347},[791],[568,2349,2351,2365,2373],{"className":2350,"style":1535},[795],[568,2352,2353,2356],{"style":1538},[568,2354],{"className":2355,"style":1542},[803],[568,2357,2359],{"className":2358},[808,809,810,811],[568,2360,2362],{"className":2361},[621,811],[568,2363,1483],{"className":2364},[621,811],[568,2366,2367,2370],{"style":1554},[568,2368],{"className":2369,"style":1542},[803],[568,2371],{"className":2372,"style":1562},[1561],[568,2374,2375,2378],{"style":1565},[568,2376],{"className":2377,"style":1542},[803],[568,2379,2381],{"className":2380},[808,809,810,811],[568,2382,2384],{"className":2383},[621,811],[568,2385,1763],{"className":2386},[621,811],[568,2388,1059],{"className":2389},[1058],[568,2391,2393],{"className":2392},[791],[568,2394,2396],{"className":2395,"style":1587},[795],[568,2397],{},[568,2399],{"className":2400},[776,1522],[568,2402,2404],{"className":2403,"style":1848},[776,1847],[568,2405,730],{"className":2406},[1852,1853],[568,2408,2410],{"className":2409},[783],[568,2411,2413],{"className":2412},[787],[568,2414,2416],{"className":2415},[791],[568,2417,2419],{"className":2418,"style":2209},[795],[568,2420,2421,2424],{"style":2212},[568,2422],{"className":2423,"style":804},[803],[568,2425,2427],{"className":2426},[808,809,810,811],[568,2428,2430],{"className":2429},[621,811],[568,2431,1999],{"className":2432},[621,811],[568,2434],{"className":2435,"style":992},[625],[568,2437,1770],{"className":2438},[996],[568,2440],{"className":2441,"style":992},[625],[568,2443,2445,2448,2451,2457],{"className":2444},[612],[568,2446],{"className":2447,"style":1698},[616],[568,2449,1315],{"className":2450},[621],[568,2452,2454],{"className":2453},[621],[568,2455,1709],{"className":2456},[1708],[568,2458,2460],{"className":2459},[621],"8878"," reicht nicht.",[564,2463,2464,2465,2504,2505,2545],{},"Ein Los gewinnt mit ",[568,2466,2468,2486],{"className":2467},[571],[568,2469,2471],{"className":2470},[575],[577,2472,2473],{"xmlns":579},[581,2474,2475,2483],{},[584,2476,2477,2479,2481],{},[587,2478,1763],{},[591,2480,593],{},[595,2482,598],{"mathvariant":597},[600,2484,2485],{"encoding":602},"5\\,\\%",[568,2487,2489],{"className":2488,"ariaHidden":608},[607],[568,2490,2492,2495,2498,2501],{"className":2491},[612],[568,2493],{"className":2494,"style":617},[616],[568,2496,1763],{"className":2497},[621],[568,2499],{"className":2500,"style":626},[625],[568,2502,598],{"className":2503},[621],". Wie viele Lose braucht man, um mit mindestens ",[568,2506,2508,2527],{"className":2507},[571],[568,2509,2511],{"className":2510},[575],[577,2512,2513],{"xmlns":579},[581,2514,2515,2524],{},[584,2516,2517,2520,2522],{},[587,2518,2519],{},"99",[591,2521,593],{},[595,2523,598],{"mathvariant":597},[600,2525,2526],{"encoding":602},"99\\,\\%",[568,2528,2530],{"className":2529,"ariaHidden":608},[607],[568,2531,2533,2536,2539,2542],{"className":2532},[612],[568,2534],{"className":2535,"style":617},[616],[568,2537,2519],{"className":2538},[621],[568,2540],{"className":2541,"style":626},[625],[568,2543,598],{"className":2544},[621]," wenigstens einmal zu gewinnen?",[568,2547,2549],{"className":2548},[819],[568,2550,2552,2601],{"className":2551},[571],[568,2553,2555],{"className":2554},[575],[577,2556,2557],{"xmlns":579,"display":828},[581,2558,2559,2598],{},[584,2560,2561,2563,2565,2593,2595],{},[595,2562,645],{},[713,2564,853],{},[1477,2566,2567,2580],{},[584,2568,2569,2571,2573,2575,2578],{},[595,2570,1245],{},[713,2572,865],{},[713,2574,716],{"stretchy":715},[587,2576,2577],{},"0,01",[713,2579,730],{"stretchy":715},[584,2581,2582,2584,2586,2588,2591],{},[595,2583,1245],{},[713,2585,865],{},[713,2587,716],{"stretchy":715},[587,2589,2590],{},"0,95",[713,2592,730],{"stretchy":715},[713,2594,1770],{},[587,2596,2597],{},"89,78",[600,2599,2600],{"encoding":602},"n \\geq \\frac{\\ln(0{,}01)}{\\ln(0{,}95)} \\approx 89{,}78",[568,2602,2604,2622,2740],{"className":2603,"ariaHidden":608},[607],[568,2605,2607,2610,2613,2616,2619],{"className":2606},[612],[568,2608],{"className":2609,"style":1786},[616],[568,2611,645],{"className":2612},[621,661],[568,2614],{"className":2615,"style":992},[625],[568,2617,853],{"className":2618},[996],[568,2620],{"className":2621,"style":992},[625],[568,2623,2625,2629,2731,2734,2737],{"className":2624},[612],[568,2626],{"className":2627,"style":2628},[616],"height:2.363em;vertical-align:-0.936em;",[568,2630,2632,2635,2728],{"className":2631},[621],[568,2633],{"className":2634},[749,1522],[568,2636,2638],{"className":2637},[1477],[568,2639,2641,2719],{"className":2640},[787,1020],[568,2642,2644,2716],{"className":2643},[791],[568,2645,2647,2678,2686],{"className":2646,"style":1824},[795],[568,2648,2650,2653],{"style":2649},"top:-2.314em;",[568,2651],{"className":2652,"style":1542},[803],[568,2654,2656,2659,2662,2665,2671,2675],{"className":2655},[621],[568,2657,1245],{"className":2658},[1043],[568,2660,716],{"className":2661},[749],[568,2663,1315],{"className":2664},[621],[568,2666,2668],{"className":2667},[621],[568,2669,1709],{"className":2670},[1708],[568,2672,2674],{"className":2673},[621],"95",[568,2676,730],{"className":2677},[776],[568,2679,2680,2683],{"style":1554},[568,2681],{"className":2682,"style":1542},[803],[568,2684],{"className":2685,"style":1562},[1561],[568,2687,2688,2691],{"style":1938},[568,2689],{"className":2690,"style":1542},[803],[568,2692,2694,2697,2700,2703,2709,2713],{"className":2693},[621],[568,2695,1245],{"className":2696},[1043],[568,2698,716],{"className":2699},[749],[568,2701,1315],{"className":2702},[621],[568,2704,2706],{"className":2705},[621],[568,2707,1709],{"className":2708},[1708],[568,2710,2712],{"className":2711},[621],"01",[568,2714,730],{"className":2715},[776],[568,2717,1059],{"className":2718},[1058],[568,2720,2722],{"className":2721},[791],[568,2723,2726],{"className":2724,"style":2725},[795],"height:0.936em;",[568,2727],{},[568,2729],{"className":2730},[776,1522],[568,2732],{"className":2733,"style":992},[625],[568,2735,1770],{"className":2736},[996],[568,2738],{"className":2739,"style":992},[625],[568,2741,2743,2746,2750,2756],{"className":2742},[612],[568,2744],{"className":2745,"style":1698},[616],[568,2747,2749],{"className":2748},[621],"89",[568,2751,2753],{"className":2752},[621],[568,2754,1709],{"className":2755},[1708],[568,2757,2759],{"className":2758},[621],"78",[564,2761,2762,2763,2791,2792,2923,2924,2952,2953,2993],{},"Es sind ",[568,2764,2766,2779],{"className":2765},[571],[568,2767,2769],{"className":2768},[575],[577,2770,2771],{"xmlns":579},[581,2772,2773,2777],{},[584,2774,2775],{},[587,2776,589],{},[600,2778,589],{"encoding":602},[568,2780,2782],{"className":2781,"ariaHidden":608},[607],[568,2783,2785,2788],{"className":2784},[612],[568,2786],{"className":2787,"style":1397},[616],[568,2789,589],{"className":2790},[621]," Lose nötig: ",[568,2793,2795,2822],{"className":2794},[571],[568,2796,2798],{"className":2797},[575],[577,2799,2800],{"xmlns":579},[581,2801,2802,2819],{},[584,2803,2804,2806,2808,2814,2816],{},[587,2805,719],{},[713,2807,722],{},[726,2809,2810,2812],{},[587,2811,2590],{},[587,2813,589],{},[713,2815,1770],{},[587,2817,2818],{},"0,9901",[600,2820,2821],{"encoding":602},"1 - 0{,}95^{90} \\approx 0{,}9901",[568,2823,2825,2843,2904],{"className":2824,"ariaHidden":608},[607],[568,2826,2828,2831,2834,2837,2840],{"className":2827},[612],[568,2829],{"className":2830,"style":915},[616],[568,2832,719],{"className":2833},[621],[568,2835],{"className":2836,"style":756},[625],[568,2838,722],{"className":2839},[760],[568,2841],{"className":2842,"style":756},[625],[568,2844,2846,2850,2853,2859,2862,2895,2898,2901],{"className":2845},[612],[568,2847],{"className":2848,"style":2849},[616],"height:1.0085em;vertical-align:-0.1944em;",[568,2851,1315],{"className":2852},[621],[568,2854,2856],{"className":2855},[621],[568,2857,1709],{"className":2858},[1708],[568,2860,1713],{"className":2861},[621],[568,2863,2865,2868],{"className":2864},[621],[568,2866,1763],{"className":2867},[621],[568,2869,2871],{"className":2870},[783],[568,2872,2874],{"className":2873},[787],[568,2875,2877],{"className":2876},[791],[568,2878,2881],{"className":2879,"style":2880},[795],"height:0.8141em;",[568,2882,2883,2886],{"style":799},[568,2884],{"className":2885,"style":804},[803],[568,2887,2889],{"className":2888},[808,809,810,811],[568,2890,2892],{"className":2891},[621,811],[568,2893,589],{"className":2894},[621,811],[568,2896],{"className":2897,"style":992},[625],[568,2899,1770],{"className":2900},[996],[568,2902],{"className":2903,"style":992},[625],[568,2905,2907,2910,2913,2919],{"className":2906},[612],[568,2908],{"className":2909,"style":1698},[616],[568,2911,1315],{"className":2912},[621],[568,2914,2916],{"className":2915},[621],[568,2917,1709],{"className":2918},[1708],[568,2920,2922],{"className":2921},[621],"9901",", bei ",[568,2925,2927,2940],{"className":2926},[571],[568,2928,2930],{"className":2929},[575],[577,2931,2932],{"xmlns":579},[581,2933,2934,2938],{},[584,2935,2936],{},[587,2937,2749],{},[600,2939,2749],{"encoding":602},[568,2941,2943],{"className":2942,"ariaHidden":608},[607],[568,2944,2946,2949],{"className":2945},[612],[568,2947],{"className":2948,"style":1397},[616],[568,2950,2749],{"className":2951},[621]," Losen nur ",[568,2954,2956,2971],{"className":2955},[571],[568,2957,2959],{"className":2958},[575],[577,2960,2961],{"xmlns":579},[581,2962,2963,2968],{},[584,2964,2965],{},[587,2966,2967],{},"0,9896",[600,2969,2970],{"encoding":602},"0{,}9896",[568,2972,2974],{"className":2973,"ariaHidden":608},[607],[568,2975,2977,2980,2983,2989],{"className":2976},[612],[568,2978],{"className":2979,"style":1698},[616],[568,2981,1315],{"className":2982},[621],[568,2984,2986],{"className":2985},[621],[568,2987,1709],{"className":2988},[1708],[568,2990,2992],{"className":2991},[621],"9896",".",[559,2995,2997],{"id":2996},"typische-fehler","Typische Fehler",[2999,3000,3001,3127,3298,3516],"ul",{},[3002,3003,3004,3005,3072,3073,3126],"li",{},"Beim Teilen durch ",[568,3006,3008,3033],{"className":3007},[571],[568,3009,3011],{"className":3010},[575],[577,3012,3013],{"xmlns":579},[581,3014,3015,3031],{},[584,3016,3017,3019,3021,3023,3025,3027,3029],{},[595,3018,1245],{},[713,3020,865],{},[713,3022,716],{"stretchy":715},[587,3024,719],{},[713,3026,722],{},[595,3028,564],{},[713,3030,730],{"stretchy":715},[600,3032,1260],{"encoding":602},[568,3034,3036,3060],{"className":3035,"ariaHidden":608},[607],[568,3037,3039,3042,3045,3048,3051,3054,3057],{"className":3038},[612],[568,3040],{"className":3041,"style":745},[616],[568,3043,1245],{"className":3044},[1043],[568,3046,716],{"className":3047},[749],[568,3049,719],{"className":3050},[621],[568,3052],{"className":3053,"style":756},[625],[568,3055,722],{"className":3056},[760],[568,3058],{"className":3059,"style":756},[625],[568,3061,3063,3066,3069],{"className":3062},[612],[568,3064],{"className":3065,"style":745},[616],[568,3067,564],{"className":3068},[621,661],[568,3070,730],{"className":3071},[776]," das Ungleichheitszeichen nicht umdrehen. Dann erhält man ",[568,3074,3076,3095],{"className":3075},[571],[568,3077,3079],{"className":3078},[575],[577,3080,3081],{"xmlns":579},[581,3082,3083,3092],{},[584,3084,3085,3087,3089],{},[595,3086,645],{},[713,3088,890],{},[713,3090,3091],{},"…",[600,3093,3094],{"encoding":602},"n \\leq \\ldots",[568,3096,3098,3116],{"className":3097,"ariaHidden":608},[607],[568,3099,3101,3104,3107,3110,3113],{"className":3100},[612],[568,3102],{"className":3103,"style":1786},[616],[568,3105,645],{"className":3106},[621,661],[568,3108],{"className":3109,"style":992},[625],[568,3111,890],{"className":3112},[996],[568,3114],{"className":3115,"style":992},[625],[568,3117,3119,3123],{"className":3118},[612],[568,3120],{"className":3121,"style":3122},[616],"height:0.123em;",[568,3124,3091],{"className":3125},[1843],", was keinen Sinn ergibt.",[3002,3128,3129,3130,3168,3169,2923,3197,3236,3237,3265,3266,3269,3270,2993],{},"Kaufmännisch runden. Bei ",[568,3131,3133,3147],{"className":3132},[571],[568,3134,3136],{"className":3135},[575],[577,3137,3138],{"xmlns":579},[581,3139,3140,3144],{},[584,3141,3142],{},[587,3143,1773],{},[600,3145,3146],{"encoding":602},"12{,}63",[568,3148,3150],{"className":3149,"ariaHidden":608},[607],[568,3151,3153,3156,3159,3165],{"className":3152},[612],[568,3154],{"className":3155,"style":1698},[616],[568,3157,1999],{"className":3158},[621],[568,3160,3162],{"className":3161},[621],[568,3163,1709],{"className":3164},[1708],[568,3166,2009],{"className":3167},[621]," ergibt das zufällig ",[568,3170,3172,3185],{"className":3171},[571],[568,3173,3175],{"className":3174},[575],[577,3176,3177],{"xmlns":579},[581,3178,3179,3183],{},[584,3180,3181],{},[587,3182,2027],{},[600,3184,2027],{"encoding":602},[568,3186,3188],{"className":3187,"ariaHidden":608},[607],[568,3189,3191,3194],{"className":3190},[612],[568,3192],{"className":3193,"style":1397},[616],[568,3195,2027],{"className":3196},[621],[568,3198,3200,3215],{"className":3199},[571],[568,3201,3203],{"className":3202},[575],[577,3204,3205],{"xmlns":579},[581,3206,3207,3212],{},[584,3208,3209],{},[587,3210,3211],{},"12,1",[600,3213,3214],{"encoding":602},"12{,}1",[568,3216,3218],{"className":3217,"ariaHidden":608},[607],[568,3219,3221,3224,3227,3233],{"className":3220},[612],[568,3222],{"className":3223,"style":1698},[616],[568,3225,1999],{"className":3226},[621],[568,3228,3230],{"className":3229},[621],[568,3231,1709],{"className":3232},[1708],[568,3234,719],{"className":3235},[621]," aber ",[568,3238,3240,3253],{"className":3239},[571],[568,3241,3243],{"className":3242},[575],[577,3244,3245],{"xmlns":579},[581,3246,3247,3251],{},[584,3248,3249],{},[587,3250,1999],{},[600,3252,1999],{"encoding":602},[568,3254,3256],{"className":3255,"ariaHidden":608},[607],[568,3257,3259,3262],{"className":3258},[612],[568,3260],{"className":3261,"style":1397},[616],[568,3263,1999],{"className":3264},[621],", und das reicht nicht. Es wird immer ",[667,3267,3268],{},"aufgerundet",", hier also auf ",[568,3271,3273,3286],{"className":3272},[571],[568,3274,3276],{"className":3275},[575],[577,3277,3278],{"xmlns":579},[581,3279,3280,3284],{},[584,3281,3282],{},[587,3283,2027],{},[600,3285,2027],{"encoding":602},[568,3287,3289],{"className":3288,"ariaHidden":608},[607],[568,3290,3292,3295],{"className":3291},[612],[568,3293],{"className":3294,"style":1397},[616],[568,3296,2027],{"className":3297},[621],[3002,3299,3300,3301,3361,3362,3452,3453,3511,3512,3515],{},"Mit ",[568,3302,3304,3322],{"className":3303},[571],[568,3305,3307],{"className":3306},[575],[577,3308,3309],{"xmlns":579},[581,3310,3311,3319],{},[584,3312,3313],{},[726,3314,3315,3317],{},[595,3316,564],{},[595,3318,645],{},[600,3320,3321],{"encoding":602},"p^n",[568,3323,3325],{"className":3324,"ariaHidden":608},[607],[568,3326,3328,3332],{"className":3327},[612],[568,3329],{"className":3330,"style":3331},[616],"height:0.8588em;vertical-align:-0.1944em;",[568,3333,3335,3338],{"className":3334},[621],[568,3336,564],{"className":3337},[621,661],[568,3339,3341],{"className":3340},[783],[568,3342,3344],{"className":3343},[787],[568,3345,3347],{"className":3346},[791],[568,3348,3350],{"className":3349,"style":796},[795],[568,3351,3352,3355],{"style":799},[568,3353],{"className":3354,"style":804},[803],[568,3356,3358],{"className":3357},[808,809,810,811],[568,3359,645],{"className":3360},[621,661,811]," statt ",[568,3363,3365,3390],{"className":3364},[571],[568,3366,3368],{"className":3367},[575],[577,3369,3370],{"xmlns":579},[581,3371,3372,3388],{},[584,3373,3374,3376,3378,3380,3382],{},[713,3375,716],{"stretchy":715},[587,3377,719],{},[713,3379,722],{},[595,3381,564],{},[726,3383,3384,3386],{},[713,3385,730],{"stretchy":715},[595,3387,645],{},[600,3389,735],{"encoding":602},[568,3391,3393,3414],{"className":3392,"ariaHidden":608},[607],[568,3394,3396,3399,3402,3405,3408,3411],{"className":3395},[612],[568,3397],{"className":3398,"style":745},[616],[568,3400,716],{"className":3401},[749],[568,3403,719],{"className":3404},[621],[568,3406],{"className":3407,"style":756},[625],[568,3409,722],{"className":3410},[760],[568,3412],{"className":3413,"style":756},[625],[568,3415,3417,3420,3423],{"className":3416},[612],[568,3418],{"className":3419,"style":745},[616],[568,3421,564],{"className":3422},[621,661],[568,3424,3426,3429],{"className":3425},[776],[568,3427,730],{"className":3428},[776],[568,3430,3432],{"className":3431},[783],[568,3433,3435],{"className":3434},[787],[568,3436,3438],{"className":3437},[791],[568,3439,3441],{"className":3440,"style":796},[795],[568,3442,3443,3446],{"style":799},[568,3444],{"className":3445,"style":804},[803],[568,3447,3449],{"className":3448},[808,809,810,811],[568,3450,645],{"className":3451},[621,661,811]," rechnen. ",[568,3454,3456,3473],{"className":3455},[571],[568,3457,3459],{"className":3458},[575],[577,3460,3461],{"xmlns":579},[581,3462,3463,3471],{},[584,3464,3465],{},[726,3466,3467,3469],{},[595,3468,564],{},[595,3470,645],{},[600,3472,3321],{"encoding":602},[568,3474,3476],{"className":3475,"ariaHidden":608},[607],[568,3477,3479,3482],{"className":3478},[612],[568,3480],{"className":3481,"style":3331},[616],[568,3483,3485,3488],{"className":3484},[621],[568,3486,564],{"className":3487},[621,661],[568,3489,3491],{"className":3490},[783],[568,3492,3494],{"className":3493},[787],[568,3495,3497],{"className":3496},[791],[568,3498,3500],{"className":3499,"style":796},[795],[568,3501,3502,3505],{"style":799},[568,3503],{"className":3504,"style":804},[803],[568,3506,3508],{"className":3507},[808,809,810,811],[568,3509,645],{"className":3510},[621,661,811]," ist die Wahrscheinlichkeit, dass ",[667,3513,3514],{},"jeder"," Versuch ein Treffer ist.",[3002,3517,3518,3519,3640,3641,3669],{},"Die Wahrscheinlichkeiten addieren: ",[568,3520,3522,3545],{"className":3521},[571],[568,3523,3525],{"className":3524},[575],[577,3526,3527],{"xmlns":579},[581,3528,3529,3542],{},[584,3530,3531,3533,3536],{},[587,3532,2027],{},[713,3534,3535],{},"⋅",[1477,3537,3538,3540],{},[587,3539,719],{},[587,3541,1483],{},[600,3543,3544],{"encoding":602},"13 \\cdot \\frac{1}{6}",[568,3546,3548,3566],{"className":3547,"ariaHidden":608},[607],[568,3549,3551,3554,3557,3560,3563],{"className":3550},[612],[568,3552],{"className":3553,"style":1397},[616],[568,3555,2027],{"className":3556},[621],[568,3558],{"className":3559,"style":756},[625],[568,3561,3535],{"className":3562},[760],[568,3564],{"className":3565,"style":756},[625],[568,3567,3569,3572],{"className":3568},[612],[568,3570],{"className":3571,"style":1515},[616],[568,3573,3575,3578,3637],{"className":3574},[621],[568,3576],{"className":3577},[749,1522],[568,3579,3581],{"className":3580},[1477],[568,3582,3584,3629],{"className":3583},[787,1020],[568,3585,3587,3626],{"className":3586},[791],[568,3588,3590,3604,3612],{"className":3589,"style":1535},[795],[568,3591,3592,3595],{"style":1538},[568,3593],{"className":3594,"style":1542},[803],[568,3596,3598],{"className":3597},[808,809,810,811],[568,3599,3601],{"className":3600},[621,811],[568,3602,1483],{"className":3603},[621,811],[568,3605,3606,3609],{"style":1554},[568,3607],{"className":3608,"style":1542},[803],[568,3610],{"className":3611,"style":1562},[1561],[568,3613,3614,3617],{"style":1565},[568,3615],{"className":3616,"style":1542},[803],[568,3618,3620],{"className":3619},[808,809,810,811],[568,3621,3623],{"className":3622},[621,811],[568,3624,719],{"className":3625},[621,811],[568,3627,1059],{"className":3628},[1058],[568,3630,3632],{"className":3631},[791],[568,3633,3635],{"className":3634,"style":1587},[795],[568,3636],{},[568,3638],{"className":3639},[776,1522]," ist größer als ",[568,3642,3644,3657],{"className":3643},[571],[568,3645,3647],{"className":3646},[575],[577,3648,3649],{"xmlns":579},[581,3650,3651,3655],{},[584,3652,3653],{},[587,3654,719],{},[600,3656,719],{"encoding":602},[568,3658,3660],{"className":3659,"ariaHidden":608},[607],[568,3661,3663,3666],{"className":3662},[612],[568,3664],{"className":3665,"style":1397},[616],[568,3667,719],{"className":3668},[621]," und keine Wahrscheinlichkeit.",{"title":3671,"searchDepth":3672,"depth":3672,"links":3673},"",2,[3674,3675,3676],{"id":561,"depth":3672,"text":562},{"id":1415,"depth":3672,"text":1416},{"id":2996,"depth":3672,"text":2997},[3678,3681,3684,3687,3690,3693,3696],{"lhs":3679,"rhs":3680},"1 - (1 - 0.2)^(log(1 - 0.9) \u002F log(1 - 0.2))","0.9",{"lhs":3682,"rhs":3683},"round(log(0.1) \u002F log(5\u002F6), 2)","12.63",{"lhs":3685,"rhs":3686},"round(1 - (5\u002F6)^13, 4)","0.9065",{"lhs":3688,"rhs":3689},"round(1 - (5\u002F6)^12, 4)","0.8878",{"lhs":3691,"rhs":3692},"round(log(0.01) \u002F log(0.95), 2)","89.78",{"lhs":3694,"rhs":3695},"round(1 - 0.95^90, 4)","0.9901",{"lhs":3697,"rhs":3698},"round(1 - 0.95^89, 4)","0.9896","0 \u003C p \u003C 1,\\ 0 \u003C P_{\\min} \u003C 1,\\ n \\in \\mathbb{N}","\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 < 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:0.7335em;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>\u003Cmn>0\u003C\u002Fmn>\u003Cmo><\u003C\u002Fmo>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>min\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmsub>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 < P_{\\min} < 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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3175em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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=\"mop mtight\">\u003Cspan class=\"mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mtight\">n\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.8389em;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>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{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:0.5782em;vertical-align:-0.0391em;\">\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","at-least-one","1 - (1-p)^n \\geq P_{\\min} \\iff n \\geq \\frac{\\ln(1 - P_{\\min})}{\\ln(1-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>\u003Cmn>1\u003C\u002Fmn>\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>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>≥\u003C\u002Fmo>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>min\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmsub>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>ln\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>min\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>ln\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 - (1-p)^n \\geq P_{\\min} \\iff n \\geq \\frac{\\ln(1 - P_{\\min})}{\\ln(1-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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:1em;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:0.7144em;\">\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 mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3175em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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=\"mop mtight\">\u003Cspan class=\"mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mtight\">n\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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>\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:2.363em;vertical-align:-0.936em;\">\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:1.427em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">ln\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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 mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">ln\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3175em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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=\"mop mtight\">\u003Cspan class=\"mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mtight\">n\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.936em;\">\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\u002Fmindestens-einmal-aufgabe",[],[3712,3713,3714],"complement-probability","binomial-distribution","log-definition",{"title":548,"description":3671},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmindestens-einmal-aufgabe","Wie viele Versuche braucht man, um mit einer Mindestwahrscheinlichkeit wenigstens einen Treffer zu erzielen?",[3719,3720,3721,3722,3723],"gegenereignis","mindestens einmal","logarithmus","bernoulli-kette","stichprobenumfang",[3725,3728,3731,3735],{"symbol":564,"meaning":3726,"symbolHtml":3727},"Trefferwahrscheinlichkeit bei jedem einzelnen 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>",{"symbol":645,"meaning":3729,"symbolHtml":3730},"Anzahl der Versuche, gesucht ist die kleinste passende","\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":3732,"meaning":3733,"symbolHtml":3734},"P_{\\min}","geforderte Mindestwahrscheinlichkeit für mindestens einen Treffer","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>min\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P_{\\min}\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3175em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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=\"mop mtight\">\u003Cspan class=\"mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mtight\">n\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":735,"meaning":3736,"symbolHtml":3737},"Wahrscheinlichkeit, in n Versuchen keinen einzigen Treffer zu haben","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(1-p)^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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:1em;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:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","QLU0yDff7pG5OYUYOk-0QWxVHkeLBoCGT3dlAPh7PrY",[3740,3743,3746],{"stem":3741,"title":3742,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Flogarithmus-definition","Definition des Logarithmus",{"stem":3744,"title":3745,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":3747,"title":3748,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit","Gegenwahrscheinlichkeit",1793824286617]