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Die Wahrscheinlichkeit, dass ",[568,793,795,812],{"className":794},[571],[568,796,798],{"className":797},[575],[577,799,800],{"xmlns":579},[581,801,802,810],{},[584,803,804],{},[648,805,806,808],{},[595,807,652],{},[595,809,655],{},[600,811,658],{"encoding":602},[568,813,815],{"className":814,"ariaHidden":608},[607],[568,816,818,821],{"className":817},[612],[568,819],{"className":820,"style":668},[616],[568,822,824,827],{"className":823},[621],[568,825,652],{"className":826},[621,675],[568,828,830],{"className":829},[679],[568,831,833,853],{"className":832},[683,684],[568,834,836,850],{"className":835},[688],[568,837,839],{"className":838,"style":693},[692],[568,840,841,844],{"style":696},[568,842],{"className":843,"style":701},[700],[568,845,847],{"className":846},[705,706,707,708],[568,848,655],{"className":849},[621,675,708],[568,851,716],{"className":852},[715],[568,854,856],{"className":855},[688],[568,857,859],{"className":858,"style":723},[692],[568,860],{}," um weniger als ",[568,863,865,878],{"className":864},[571],[568,866,868],{"className":867},[575],[577,869,870],{"xmlns":579},[581,871,872,876],{},[584,873,874],{},[595,875,774],{},[600,877,777],{"encoding":602},[568,879,881],{"className":880,"ariaHidden":608},[607],[568,882,884,887],{"className":883},[612],[568,885],{"className":886,"style":787},[616],[568,888,774],{"className":889},[621,675]," von ",[568,892,894,907],{"className":893},[571],[568,895,897],{"className":896},[575],[577,898,899],{"xmlns":579},[581,900,901,905],{},[584,902,903],{},[595,904,564],{},[600,906,564],{"encoding":602},[568,908,910],{"className":909,"ariaHidden":608},[607],[568,911,913,916],{"className":912},[612],[568,914],{"className":915,"style":752},[616],[568,917,564],{"className":918},[621,675]," abweicht, strebt für ",[568,921,923,944],{"className":922},[571],[568,924,926],{"className":925},[575],[577,927,928],{"xmlns":579},[581,929,930,941],{},[584,931,932,934,938],{},[595,933,655],{},[935,936,937],"mo",{},"→",[595,939,940],{"mathvariant":597},"∞",[600,942,943],{"encoding":602},"n \\to \\infty",[568,945,947,967],{"className":946,"ariaHidden":608},[607],[568,948,950,953,956,960,964],{"className":949},[612],[568,951],{"className":952,"style":787},[616],[568,954,655],{"className":955},[621,675],[568,957],{"className":958,"style":959},[625],"margin-right:0.2778em;",[568,961,937],{"className":962},[963],"mrel",[568,965],{"className":966,"style":959},[625],[568,968,970,973],{"className":969},[612],[568,971],{"className":972,"style":787},[616],[568,974,940],{"className":975},[621]," gegen ",[568,978,980,994],{"className":979},[571],[568,981,983],{"className":982},[575],[577,984,985],{"xmlns":579},[581,986,987,992],{},[584,988,989],{},[587,990,991],{},"1",[600,993,991],{"encoding":602},[568,995,997],{"className":996,"ariaHidden":608},[607],[568,998,1000,1004],{"className":999},[612],[568,1001],{"className":1002,"style":1003},[616],"height:0.6444em;",[568,1005,991],{"className":1006},[621],". Größere Abweichungen sind also nicht unmöglich, werden aber immer unwahrscheinlicher.",[564,1009,1010],{},"Wie schnell das geht, zeigt die Tschebyscheff-Ungleichung:",[568,1012,1015],{"className":1013},[1014],"katex-display",[568,1016,1018,1096],{"className":1017},[571],[568,1019,1021],{"className":1020},[575],[577,1022,1024],{"xmlns":579,"display":1023},"block",[581,1025,1026,1093],{},[584,1027,1028,1031,1060,1063],{},[595,1029,1030],{},"P",[584,1032,1033,1036,1039,1045,1048,1050,1052,1055,1057],{},[935,1034,1035],{"fence":608},"(",[595,1037,1038],{"mathvariant":597},"∣",[648,1040,1041,1043],{},[595,1042,652],{},[595,1044,655],{},[935,1046,1047],{},"−",[595,1049,564],{},[595,1051,1038],{"mathvariant":597},[935,1053,1054],{},"≥",[595,1056,774],{},[935,1058,1059],{"fence":608},")",[935,1061,1062],{},"≤",[1064,1065,1066,1081],"mfrac",{},[584,1067,1068,1070,1073,1075,1077,1079],{},[595,1069,564],{},[935,1071,1035],{"stretchy":1072},"false",[587,1074,991],{},[935,1076,1047],{},[595,1078,564],{},[935,1080,1059],{"stretchy":1072},[584,1082,1083,1085],{},[595,1084,655],{},[1086,1087,1088,1090],"msup",{},[595,1089,774],{},[587,1091,1092],{},"2",[600,1094,1095],{"encoding":602},"P\\left(|h_n - p| \\geq \\varepsilon\\right) \\leq \\frac{p(1-p)}{n \\varepsilon^2}",[568,1097,1099,1208],{"className":1098,"ariaHidden":608},[607],[568,1100,1102,1106,1110,1113,1199,1202,1205],{"className":1101},[612],[568,1103],{"className":1104,"style":1105},[616],"height:1em;vertical-align:-0.25em;",[568,1107,1030],{"className":1108,"style":1109},[621,675],"margin-right:0.1389em;",[568,1111],{"className":1112,"style":626},[625],[568,1114,1117,1123,1126,1166,1170,1174,1177,1180,1183,1186,1189,1192,1195],{"className":1115},[1116],"minner",[568,1118,1035],{"className":1119,"style":1122},[1120,1121],"mopen","delimcenter","top:0em;",[568,1124,1038],{"className":1125},[621],[568,1127,1129,1132],{"className":1128},[621],[568,1130,652],{"className":1131},[621,675],[568,1133,1135],{"className":1134},[679],[568,1136,1138,1158],{"className":1137},[683,684],[568,1139,1141,1155],{"className":1140},[688],[568,1142,1144],{"className":1143,"style":693},[692],[568,1145,1146,1149],{"style":696},[568,1147],{"className":1148,"style":701},[700],[568,1150,1152],{"className":1151},[705,706,707,708],[568,1153,655],{"className":1154},[621,675,708],[568,1156,716],{"className":1157},[715],[568,1159,1161],{"className":1160},[688],[568,1162,1164],{"className":1163,"style":723},[692],[568,1165],{},[568,1167],{"className":1168,"style":1169},[625],"margin-right:0.2222em;",[568,1171,1047],{"className":1172},[1173],"mbin",[568,1175],{"className":1176,"style":1169},[625],[568,1178,564],{"className":1179},[621,675],[568,1181,1038],{"className":1182},[621],[568,1184],{"className":1185,"style":959},[625],[568,1187,1054],{"className":1188},[963],[568,1190],{"className":1191,"style":959},[625],[568,1193,774],{"className":1194},[621,675],[568,1196,1059],{"className":1197,"style":1122},[1198,1121],"mclose",[568,1200],{"className":1201,"style":959},[625],[568,1203,1062],{"className":1204},[963],[568,1206],{"className":1207,"style":959},[625],[568,1209,1211,1215],{"className":1210},[612],[568,1212],{"className":1213,"style":1214},[616],"height:2.113em;vertical-align:-0.686em;",[568,1216,1218,1222,1335],{"className":1217},[621],[568,1219],{"className":1220},[1120,1221],"nulldelimiter",[568,1223,1225],{"className":1224},[1064],[568,1226,1228,1326],{"className":1227},[683,684],[568,1229,1231,1323],{"className":1230},[688],[568,1232,1235,1279,1290],{"className":1233,"style":1234},[692],"height:1.427em;",[568,1236,1238,1242],{"style":1237},"top:-2.314em;",[568,1239],{"className":1240,"style":1241},[700],"height:3em;",[568,1243,1245,1248],{"className":1244},[621],[568,1246,655],{"className":1247},[621,675],[568,1249,1251,1254],{"className":1250},[621],[568,1252,774],{"className":1253},[621,675],[568,1255,1257],{"className":1256},[679],[568,1258,1260],{"className":1259},[683],[568,1261,1263],{"className":1262},[688],[568,1264,1267],{"className":1265,"style":1266},[692],"height:0.7401em;",[568,1268,1270,1273],{"style":1269},"top:-2.989em;margin-right:0.05em;",[568,1271],{"className":1272,"style":701},[700],[568,1274,1276],{"className":1275},[705,706,707,708],[568,1277,1092],{"className":1278},[621,708],[568,1280,1282,1285],{"style":1281},"top:-3.23em;",[568,1283],{"className":1284,"style":1241},[700],[568,1286],{"className":1287,"style":1289},[1288],"frac-line","border-bottom-width:0.04em;",[568,1291,1293,1296],{"style":1292},"top:-3.677em;",[568,1294],{"className":1295,"style":1241},[700],[568,1297,1299,1302,1305,1308,1311,1314,1317,1320],{"className":1298},[621],[568,1300,564],{"className":1301},[621,675],[568,1303,1035],{"className":1304},[1120],[568,1306,991],{"className":1307},[621],[568,1309],{"className":1310,"style":1169},[625],[568,1312,1047],{"className":1313},[1173],[568,1315],{"className":1316,"style":1169},[625],[568,1318,564],{"className":1319},[621,675],[568,1321,1059],{"className":1322},[1198],[568,1324,716],{"className":1325},[715],[568,1327,1329],{"className":1328},[688],[568,1330,1333],{"className":1331,"style":1332},[692],"height:0.686em;",[568,1334],{},[568,1336],{"className":1337},[1198,1221],[564,1339,1340],{},"Das Gesetz begründet, warum man Wahrscheinlichkeiten über relative Häufigkeiten schätzen kann. Es sagt aber nichts über einzelne Versuche: Eine Münze „merkt sich“ nicht, wie oft schon Kopf kam.",[559,1342,1344],{"id":1343},"beispiele","Beispiele",[564,1346,1347,1348,1377,1378,1445,1446,1545,1546,890,1586,1624],{},"Eine faire Münze wird ",[568,1349,1351,1365],{"className":1350},[571],[568,1352,1354],{"className":1353},[575],[577,1355,1356],{"xmlns":579},[581,1357,1358,1363],{},[584,1359,1360],{},[587,1361,1362],{},"1000",[600,1364,1362],{"encoding":602},[568,1366,1368],{"className":1367,"ariaHidden":608},[607],[568,1369,1371,1374],{"className":1370},[612],[568,1372],{"className":1373,"style":1003},[616],[568,1375,1362],{"className":1376},[621],"-mal geworfen, ",[568,1379,1381,1401],{"className":1380},[571],[568,1382,1384],{"className":1383},[575],[577,1385,1386],{"xmlns":579},[581,1387,1388,1398],{},[584,1389,1390,1392,1395],{},[595,1391,564],{},[935,1393,1394],{},"=",[587,1396,1397],{},"0,5",[600,1399,1400],{"encoding":602},"p = 0{,}5",[568,1402,1404,1422],{"className":1403,"ariaHidden":608},[607],[568,1405,1407,1410,1413,1416,1419],{"className":1406},[612],[568,1408],{"className":1409,"style":752},[616],[568,1411,564],{"className":1412},[621,675],[568,1414],{"className":1415,"style":959},[625],[568,1417,1394],{"className":1418},[963],[568,1420],{"className":1421,"style":959},[625],[568,1423,1425,1429,1433,1441],{"className":1424},[612],[568,1426],{"className":1427,"style":1428},[616],"height:0.8389em;vertical-align:-0.1944em;",[568,1430,1432],{"className":1431},[621],"0",[568,1434,1436],{"className":1435},[621],[568,1437,1440],{"className":1438},[1439],"mpunct",",",[568,1442,1444],{"className":1443},[621],"5",", also ",[568,1447,1449,1478],{"className":1448},[571],[568,1450,1452],{"className":1451},[575],[577,1453,1454],{"xmlns":579},[581,1455,1456,1475],{},[584,1457,1458,1460,1462,1464,1466,1468,1470,1472],{},[595,1459,564],{},[935,1461,1035],{"stretchy":1072},[587,1463,991],{},[935,1465,1047],{},[595,1467,564],{},[935,1469,1059],{"stretchy":1072},[935,1471,1394],{},[587,1473,1474],{},"0,25",[600,1476,1477],{"encoding":602},"p(1-p) = 0{,}25",[568,1479,1481,1505,1526],{"className":1480,"ariaHidden":608},[607],[568,1482,1484,1487,1490,1493,1496,1499,1502],{"className":1483},[612],[568,1485],{"className":1486,"style":1105},[616],[568,1488,564],{"className":1489},[621,675],[568,1491,1035],{"className":1492},[1120],[568,1494,991],{"className":1495},[621],[568,1497],{"className":1498,"style":1169},[625],[568,1500,1047],{"className":1501},[1173],[568,1503],{"className":1504,"style":1169},[625],[568,1506,1508,1511,1514,1517,1520,1523],{"className":1507},[612],[568,1509],{"className":1510,"style":1105},[616],[568,1512,564],{"className":1513},[621,675],[568,1515,1059],{"className":1516},[1198],[568,1518],{"className":1519,"style":959},[625],[568,1521,1394],{"className":1522},[963],[568,1524],{"className":1525,"style":959},[625],[568,1527,1529,1532,1535,1541],{"className":1528},[612],[568,1530],{"className":1531,"style":1428},[616],[568,1533,1432],{"className":1534},[621],[568,1536,1538],{"className":1537},[621],[568,1539,1440],{"className":1540},[1439],[568,1542,1544],{"className":1543},[621],"25",". Wie wahrscheinlich weicht der Anteil „Kopf“ um mindestens ",[568,1547,1549,1564],{"className":1548},[571],[568,1550,1552],{"className":1551},[575],[577,1553,1554],{"xmlns":579},[581,1555,1556,1561],{},[584,1557,1558],{},[587,1559,1560],{},"0,05",[600,1562,1563],{"encoding":602},"0{,}05",[568,1565,1567],{"className":1566,"ariaHidden":608},[607],[568,1568,1570,1573,1576,1582],{"className":1569},[612],[568,1571],{"className":1572,"style":1428},[616],[568,1574,1432],{"className":1575},[621],[568,1577,1579],{"className":1578},[621],[568,1580,1440],{"className":1581},[1439],[568,1583,1585],{"className":1584},[621],"05",[568,1587,1589,1603],{"className":1588},[571],[568,1590,1592],{"className":1591},[575],[577,1593,1594],{"xmlns":579},[581,1595,1596,1600],{},[584,1597,1598],{},[587,1599,1397],{},[600,1601,1602],{"encoding":602},"0{,}5",[568,1604,1606],{"className":1605,"ariaHidden":608},[607],[568,1607,1609,1612,1615,1621],{"className":1608},[612],[568,1610],{"className":1611,"style":1428},[616],[568,1613,1432],{"className":1614},[621],[568,1616,1618],{"className":1617},[621],[568,1619,1440],{"className":1620},[1439],[568,1622,1444],{"className":1623},[621]," ab?",[568,1626,1628],{"className":1627},[1014],[568,1629,1631,1693],{"className":1630},[571],[568,1632,1634],{"className":1633},[575],[577,1635,1636],{"xmlns":579,"display":1023},[581,1637,1638,1690],{},[584,1639,1640,1642,1666,1668,1685,1687],{},[595,1641,1030],{},[584,1643,1644,1646,1648,1654,1656,1658,1660,1662,1664],{},[935,1645,1035],{"fence":608},[595,1647,1038],{"mathvariant":597},[648,1649,1650,1652],{},[595,1651,652],{},[587,1653,1362],{},[935,1655,1047],{},[587,1657,1397],{},[595,1659,1038],{"mathvariant":597},[935,1661,1054],{},[587,1663,1560],{},[935,1665,1059],{"fence":608},[935,1667,1062],{},[1064,1669,1670,1672],{},[587,1671,1474],{},[584,1673,1674,1676,1679],{},[587,1675,1362],{},[935,1677,1678],{},"⋅",[1086,1680,1681,1683],{},[587,1682,1560],{},[587,1684,1092],{},[935,1686,1394],{},[587,1688,1689],{},"0,1",[600,1691,1692],{"encoding":602},"P\\left(|h_{1000} - 0{,}5| \\geq 0{,}05\\right) \\leq \\frac{0{,}25}{1000 \\cdot 0{,}05^2} = 0{,}1",[568,1694,1696,1816,1955],{"className":1695,"ariaHidden":608},[607],[568,1697,1699,1702,1705,1708,1807,1810,1813],{"className":1698},[612],[568,1700],{"className":1701,"style":1105},[616],[568,1703,1030],{"className":1704,"style":1109},[621,675],[568,1706],{"className":1707,"style":626},[625],[568,1709,1711,1714,1717,1761,1764,1767,1770,1773,1779,1783,1786,1789,1792,1795,1801,1804],{"className":1710},[1116],[568,1712,1035],{"className":1713,"style":1122},[1120,1121],[568,1715,1038],{"className":1716},[621],[568,1718,1720,1723],{"className":1719},[621],[568,1721,652],{"className":1722},[621,675],[568,1724,1726],{"className":1725},[679],[568,1727,1729,1753],{"className":1728},[683,684],[568,1730,1732,1750],{"className":1731},[688],[568,1733,1736],{"className":1734,"style":1735},[692],"height:0.3011em;",[568,1737,1738,1741],{"style":696},[568,1739],{"className":1740,"style":701},[700],[568,1742,1744],{"className":1743},[705,706,707,708],[568,1745,1747],{"className":1746},[621,708],[568,1748,1362],{"className":1749},[621,708],[568,1751,716],{"className":1752},[715],[568,1754,1756],{"className":1755},[688],[568,1757,1759],{"className":1758,"style":723},[692],[568,1760],{},[568,1762],{"className":1763,"style":1169},[625],[568,1765,1047],{"className":1766},[1173],[568,1768],{"className":1769,"style":1169},[625],[568,1771,1432],{"className":1772},[621],[568,1774,1776],{"className":1775},[621],[568,1777,1440],{"className":1778},[1439],[568,1780,1782],{"className":1781},[621],"5∣",[568,1784],{"className":1785,"style":959},[625],[568,1787,1054],{"className":1788},[963],[568,1790],{"className":1791,"style":959},[625],[568,1793,1432],{"className":1794},[621],[568,1796,1798],{"className":1797},[621],[568,1799,1440],{"className":1800},[1439],[568,1802,1585],{"className":1803},[621],[568,1805,1059],{"className":1806,"style":1122},[1198,1121],[568,1808],{"className":1809,"style":959},[625],[568,1811,1062],{"className":1812},[963],[568,1814],{"className":1815,"style":959},[625],[568,1817,1819,1823,1946,1949,1952],{"className":1818},[612],[568,1820],{"className":1821,"style":1822},[616],"height:2.2019em;vertical-align:-0.8804em;",[568,1824,1826,1829,1943],{"className":1825},[621],[568,1827],{"className":1828},[1120,1221],[568,1830,1832],{"className":1831},[1064],[568,1833,1835,1934],{"className":1834},[683,684],[568,1836,1838,1931],{"className":1837},[688],[568,1839,1842,1903,1911],{"className":1840,"style":1841},[692],"height:1.3214em;",[568,1843,1844,1847],{"style":1237},[568,1845],{"className":1846,"style":1241},[700],[568,1848,1850,1853,1856,1859,1862,1865,1871,1874],{"className":1849},[621],[568,1851,1362],{"className":1852},[621],[568,1854],{"className":1855,"style":1169},[625],[568,1857,1678],{"className":1858},[1173],[568,1860],{"className":1861,"style":1169},[625],[568,1863,1432],{"className":1864},[621],[568,1866,1868],{"className":1867},[621],[568,1869,1440],{"className":1870},[1439],[568,1872,1432],{"className":1873},[621],[568,1875,1877,1880],{"className":1876},[621],[568,1878,1444],{"className":1879},[621],[568,1881,1883],{"className":1882},[679],[568,1884,1886],{"className":1885},[683],[568,1887,1889],{"className":1888},[688],[568,1890,1892],{"className":1891,"style":1266},[692],[568,1893,1894,1897],{"style":1269},[568,1895],{"className":1896,"style":701},[700],[568,1898,1900],{"className":1899},[705,706,707,708],[568,1901,1092],{"className":1902},[621,708],[568,1904,1905,1908],{"style":1281},[568,1906],{"className":1907,"style":1241},[700],[568,1909],{"className":1910,"style":1289},[1288],[568,1912,1913,1916],{"style":1292},[568,1914],{"className":1915,"style":1241},[700],[568,1917,1919,1922,1928],{"className":1918},[621],[568,1920,1432],{"className":1921},[621],[568,1923,1925],{"className":1924},[621],[568,1926,1440],{"className":1927},[1439],[568,1929,1544],{"className":1930},[621],[568,1932,716],{"className":1933},[715],[568,1935,1937],{"className":1936},[688],[568,1938,1941],{"className":1939,"style":1940},[692],"height:0.8804em;",[568,1942],{},[568,1944],{"className":1945},[1198,1221],[568,1947],{"className":1948,"style":959},[625],[568,1950,1394],{"className":1951},[963],[568,1953],{"className":1954,"style":959},[625],[568,1956,1958,1961,1964,1970],{"className":1957},[612],[568,1959],{"className":1960,"style":1428},[616],[568,1962,1432],{"className":1963},[621],[568,1965,1967],{"className":1966},[621],[568,1968,1440],{"className":1969},[1439],[568,1971,991],{"className":1972},[621],[564,1974,1975,1976,2016,2017,2057,2058,2098,2099,2140,2141,756],{},"Der Anteil liegt also mit mindestens ",[568,1977,1979,1998],{"className":1978},[571],[568,1980,1982],{"className":1981},[575],[577,1983,1984],{"xmlns":579},[581,1985,1986,1995],{},[584,1987,1988,1991,1993],{},[587,1989,1990],{},"90",[591,1992,593],{},[595,1994,598],{"mathvariant":597},[600,1996,1997],{"encoding":602},"90\\,\\%",[568,1999,2001],{"className":2000,"ariaHidden":608},[607],[568,2002,2004,2007,2010,2013],{"className":2003},[612],[568,2005],{"className":2006,"style":617},[616],[568,2008,1990],{"className":2009},[621],[568,2011],{"className":2012,"style":626},[625],[568,2014,598],{"className":2015},[621]," zwischen ",[568,2018,2020,2035],{"className":2019},[571],[568,2021,2023],{"className":2022},[575],[577,2024,2025],{"xmlns":579},[581,2026,2027,2032],{},[584,2028,2029],{},[587,2030,2031],{},"0,45",[600,2033,2034],{"encoding":602},"0{,}45",[568,2036,2038],{"className":2037,"ariaHidden":608},[607],[568,2039,2041,2044,2047,2053],{"className":2040},[612],[568,2042],{"className":2043,"style":1428},[616],[568,2045,1432],{"className":2046},[621],[568,2048,2050],{"className":2049},[621],[568,2051,1440],{"className":2052},[1439],[568,2054,2056],{"className":2055},[621],"45"," und ",[568,2059,2061,2076],{"className":2060},[571],[568,2062,2064],{"className":2063},[575],[577,2065,2066],{"xmlns":579},[581,2067,2068,2073],{},[584,2069,2070],{},[587,2071,2072],{},"0,55",[600,2074,2075],{"encoding":602},"0{,}55",[568,2077,2079],{"className":2078,"ariaHidden":608},[607],[568,2080,2082,2085,2088,2094],{"className":2081},[612],[568,2083],{"className":2084,"style":1428},[616],[568,2086,1432],{"className":2087},[621],[568,2089,2091],{"className":2090},[621],[568,2092,1440],{"className":2093},[1439],[568,2095,2097],{"className":2096},[621],"55",". Bei ",[568,2100,2102,2122],{"className":2101},[571],[568,2103,2105],{"className":2104},[575],[577,2106,2107],{"xmlns":579},[581,2108,2109,2119],{},[584,2110,2111,2114,2116],{},[587,2112,2113],{},"10",[591,2115,593],{},[587,2117,2118],{},"000",[600,2120,2121],{"encoding":602},"10\\,000",[568,2123,2125],{"className":2124,"ariaHidden":608},[607],[568,2126,2128,2131,2134,2137],{"className":2127},[612],[568,2129],{"className":2130,"style":1003},[616],[568,2132,2113],{"className":2133},[621],[568,2135],{"className":2136,"style":626},[625],[568,2138,2118],{"className":2139},[621]," Würfen sinkt die Schranke auf ",[568,2142,2144,2181],{"className":2143},[571],[568,2145,2147],{"className":2146},[575],[577,2148,2149],{"xmlns":579},[581,2150,2151,2178],{},[584,2152,2153,2173,2175],{},[1064,2154,2155,2157],{},[587,2156,1474],{},[584,2158,2159,2161,2163,2165,2167],{},[587,2160,2113],{},[591,2162,593],{},[587,2164,2118],{},[935,2166,1678],{},[1086,2168,2169,2171],{},[587,2170,1560],{},[587,2172,1092],{},[935,2174,1394],{},[587,2176,2177],{},"0,01",[600,2179,2180],{"encoding":602},"\\frac{0{,}25}{10\\,000 \\cdot 0{,}05^2} = 0{,}01",[568,2182,2184,2337],{"className":2183,"ariaHidden":608},[607],[568,2185,2187,2191,2328,2331,2334],{"className":2186},[612],[568,2188],{"className":2189,"style":2190},[616],"height:1.3783em;vertical-align:-0.4811em;",[568,2192,2194,2197,2325],{"className":2193},[621],[568,2195],{"className":2196},[1120,1221],[568,2198,2200],{"className":2199},[1064],[568,2201,2203,2316],{"className":2202},[683,684],[568,2204,2206,2313],{"className":2205},[688],[568,2207,2210,2281,2289],{"className":2208,"style":2209},[692],"height:0.8972em;",[568,2211,2213,2216],{"style":2212},"top:-2.655em;",[568,2214],{"className":2215,"style":1241},[700],[568,2217,2219],{"className":2218},[705,706,707,708],[568,2220,2222,2225,2229,2232,2235,2238,2244,2247],{"className":2221},[621,708],[568,2223,2113],{"className":2224},[621,708],[568,2226],{"className":2227,"style":2228},[625,708],"margin-right:0.1952em;",[568,2230,2118],{"className":2231},[621,708],[568,2233,1678],{"className":2234},[1173,708],[568,2236,1432],{"className":2237},[621,708],[568,2239,2241],{"className":2240},[621,708],[568,2242,1440],{"className":2243},[1439,708],[568,2245,1432],{"className":2246},[621,708],[568,2248,2250,2253],{"className":2249},[621,708],[568,2251,1444],{"className":2252},[621,708],[568,2254,2256],{"className":2255},[679],[568,2257,2259],{"className":2258},[683],[568,2260,2262],{"className":2261},[688],[568,2263,2266],{"className":2264,"style":2265},[692],"height:0.7463em;",[568,2267,2269,2273],{"style":2268},"top:-2.786em;margin-right:0.0714em;",[568,2270],{"className":2271,"style":2272},[700],"height:2.5em;",[568,2274,2278],{"className":2275},[705,2276,2277,708],"reset-size3","size1",[568,2279,1092],{"className":2280},[621,708],[568,2282,2283,2286],{"style":1281},[568,2284],{"className":2285,"style":1241},[700],[568,2287],{"className":2288,"style":1289},[1288],[568,2290,2292,2295],{"style":2291},"top:-3.4461em;",[568,2293],{"className":2294,"style":1241},[700],[568,2296,2298],{"className":2297},[705,706,707,708],[568,2299,2301,2304,2310],{"className":2300},[621,708],[568,2302,1432],{"className":2303},[621,708],[568,2305,2307],{"className":2306},[621,708],[568,2308,1440],{"className":2309},[1439,708],[568,2311,1544],{"className":2312},[621,708],[568,2314,716],{"className":2315},[715],[568,2317,2319],{"className":2318},[688],[568,2320,2323],{"className":2321,"style":2322},[692],"height:0.4811em;",[568,2324],{},[568,2326],{"className":2327},[1198,1221],[568,2329],{"className":2330,"style":959},[625],[568,2332,1394],{"className":2333},[963],[568,2335],{"className":2336,"style":959},[625],[568,2338,2340,2343,2346,2352],{"className":2339},[612],[568,2341],{"className":2342,"style":1428},[616],[568,2344,1432],{"className":2345},[621],[568,2347,2349],{"className":2348},[621],[568,2350,1440],{"className":2351},[1439],[568,2353,2355],{"className":2354},[621],"01",[564,2357,2358,2359,2553,2554,2583,2584,2621,2622,2660,2661,756],{},"Die Standardabweichung der relativen Häufigkeit ist ",[568,2360,2362,2395],{"className":2361},[571],[568,2363,2365],{"className":2364},[575],[577,2366,2367],{"xmlns":579},[581,2368,2369,2392],{},[584,2370,2371],{},[2372,2373,2374],"msqrt",{},[1064,2375,2376,2390],{},[584,2377,2378,2380,2382,2384,2386,2388],{},[595,2379,564],{},[935,2381,1035],{"stretchy":1072},[587,2383,991],{},[935,2385,1047],{},[595,2387,564],{},[935,2389,1059],{"stretchy":1072},[595,2391,655],{},[600,2393,2394],{"encoding":602},"\\sqrt{\\frac{p(1-p)}{n}}",[568,2396,2398],{"className":2397,"ariaHidden":608},[607],[568,2399,2401,2405],{"className":2400},[612],[568,2402],{"className":2403,"style":2404},[616],"height:1.84em;vertical-align:-0.5225em;",[568,2406,2409],{"className":2407},[621,2408],"sqrt",[568,2410,2412,2544],{"className":2411},[683,684],[568,2413,2415,2541],{"className":2414},[688],[568,2416,2419,2518],{"className":2417,"style":2418},[692],"height:1.3175em;",[568,2420,2424,2428],{"className":2421,"style":2423},[2422],"svg-align","top:-3.8em;",[568,2425],{"className":2426,"style":2427},[700],"height:3.8em;",[568,2429,2432],{"className":2430,"style":2431},[621],"padding-left:1em;",[568,2433,2435,2438,2515],{"className":2434},[621],[568,2436],{"className":2437},[1120,1221],[568,2439,2441],{"className":2440},[1064],[568,2442,2444,2506],{"className":2443},[683,684],[568,2445,2447,2503],{"className":2446},[688],[568,2448,2451,2465,2473],{"className":2449,"style":2450},[692],"height:1.01em;",[568,2452,2453,2456],{"style":2212},[568,2454],{"className":2455,"style":1241},[700],[568,2457,2459],{"className":2458},[705,706,707,708],[568,2460,2462],{"className":2461},[621,708],[568,2463,655],{"className":2464},[621,675,708],[568,2466,2467,2470],{"style":1281},[568,2468],{"className":2469,"style":1241},[700],[568,2471],{"className":2472,"style":1289},[1288],[568,2474,2476,2479],{"style":2475},"top:-3.485em;",[568,2477],{"className":2478,"style":1241},[700],[568,2480,2482],{"className":2481},[705,706,707,708],[568,2483,2485,2488,2491,2494,2497,2500],{"className":2484},[621,708],[568,2486,564],{"className":2487},[621,675,708],[568,2489,1035],{"className":2490},[1120,708],[568,2492,991],{"className":2493},[621,708],[568,2495,1047],{"className":2496},[1173,708],[568,2498,564],{"className":2499},[621,675,708],[568,2501,1059],{"className":2502},[1198,708],[568,2504,716],{"className":2505},[715],[568,2507,2509],{"className":2508},[688],[568,2510,2513],{"className":2511,"style":2512},[692],"height:0.345em;",[568,2514],{},[568,2516],{"className":2517},[1198,1221],[568,2519,2521,2524],{"style":2520},"top:-3.2775em;",[568,2522],{"className":2523,"style":2427},[700],[568,2525,2529],{"className":2526,"style":2528},[2527],"hide-tail","min-width:1.02em;height:1.88em;",[2530,2531,2537],"svg",{"xmlns":2532,"width":2533,"height":2534,"viewBox":2535,"preserveAspectRatio":2536},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.88em","0 0 400000 1944","xMinYMin slice",[2538,2539],"path",{"d":2540},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[568,2542,716],{"className":2543},[715],[568,2545,2547],{"className":2546},[688],[568,2548,2551],{"className":2549,"style":2550},[692],"height:0.5225em;",[568,2552],{},". Sie beträgt bei ",[568,2555,2557,2571],{"className":2556},[571],[568,2558,2560],{"className":2559},[575],[577,2561,2562],{"xmlns":579},[581,2563,2564,2569],{},[584,2565,2566],{},[587,2567,2568],{},"100",[600,2570,2568],{"encoding":602},[568,2572,2574],{"className":2573,"ariaHidden":608},[607],[568,2575,2577,2580],{"className":2576},[612],[568,2578],{"className":2579,"style":1003},[616],[568,2581,2568],{"className":2582},[621]," Würfen ",[568,2585,2587,2600],{"className":2586},[571],[568,2588,2590],{"className":2589},[575],[577,2591,2592],{"xmlns":579},[581,2593,2594,2598],{},[584,2595,2596],{},[587,2597,1560],{},[600,2599,1563],{"encoding":602},[568,2601,2603],{"className":2602,"ariaHidden":608},[607],[568,2604,2606,2609,2612,2618],{"className":2605},[612],[568,2607],{"className":2608,"style":1428},[616],[568,2610,1432],{"className":2611},[621],[568,2613,2615],{"className":2614},[621],[568,2616,1440],{"className":2617},[1439],[568,2619,1585],{"className":2620},[621]," und bei ",[568,2623,2625,2642],{"className":2624},[571],[568,2626,2628],{"className":2627},[575],[577,2629,2630],{"xmlns":579},[581,2631,2632,2640],{},[584,2633,2634,2636,2638],{},[587,2635,2113],{},[591,2637,593],{},[587,2639,2118],{},[600,2641,2121],{"encoding":602},[568,2643,2645],{"className":2644,"ariaHidden":608},[607],[568,2646,2648,2651,2654,2657],{"className":2647},[612],[568,2649],{"className":2650,"style":1003},[616],[568,2652,2113],{"className":2653},[621],[568,2655],{"className":2656,"style":626},[625],[568,2658,2118],{"className":2659},[621]," Würfen nur noch ",[568,2662,2664,2679],{"className":2663},[571],[568,2665,2667],{"className":2666},[575],[577,2668,2669],{"xmlns":579},[581,2670,2671,2676],{},[584,2672,2673],{},[587,2674,2675],{},"0,005",[600,2677,2678],{"encoding":602},"0{,}005",[568,2680,2682],{"className":2681,"ariaHidden":608},[607],[568,2683,2685,2688,2691,2697],{"className":2684},[612],[568,2686],{"className":2687,"style":1428},[616],[568,2689,1432],{"className":2690},[621],[568,2692,2694],{"className":2693},[621],[568,2695,1440],{"className":2696},[1439],[568,2698,2700],{"className":2699},[621],"005",[559,2702,2704],{"id":2703},"typische-fehler","Typische Fehler",[2706,2707,2708,2749,3058],"ul",{},[2709,2710,2711,2712,756],"li",{},"Glauben, nach vielen Würfen mit „Zahl“ müsse bald Kopf kommen, „damit es sich ausgleicht“. Die Versuche sind unabhängig; die Wahrscheinlichkeit bleibt bei jedem Wurf ",[568,2713,2715,2728],{"className":2714},[571],[568,2716,2718],{"className":2717},[575],[577,2719,2720],{"xmlns":579},[581,2721,2722,2726],{},[584,2723,2724],{},[587,2725,1397],{},[600,2727,1602],{"encoding":602},[568,2729,2731],{"className":2730,"ariaHidden":608},[607],[568,2732,2734,2737,2740,2746],{"className":2733},[612],[568,2735],{"className":2736,"style":1428},[616],[568,2738,1432],{"className":2739},[621],[568,2741,2743],{"className":2742},[621],[568,2744,1440],{"className":2745},[1439],[568,2747,1444],{"className":2748},[621],[2709,2750,2751,2752,2755,2756,2890,2891,3025,3026,3029,3030,756],{},"Annehmen, die ",[632,2753,2754],{},"absolute"," Abweichung werde kleiner. Die Standardabweichung der Anzahl „Kopf“ wächst von ",[568,2757,2759,2785],{"className":2758},[571],[568,2760,2762],{"className":2761},[575],[577,2763,2764],{"xmlns":579},[581,2765,2766,2782],{},[584,2767,2768,2778,2780],{},[2372,2769,2770],{},[584,2771,2772,2774,2776],{},[587,2773,2568],{},[935,2775,1678],{},[587,2777,1474],{},[935,2779,1394],{},[587,2781,1444],{},[600,2783,2784],{"encoding":602},"\\sqrt{100 \\cdot 0{,}25} = 5",[568,2786,2788,2881],{"className":2787,"ariaHidden":608},[607],[568,2789,2791,2795,2872,2875,2878],{"className":2790},[612],[568,2792],{"className":2793,"style":2794},[616],"height:1.04em;vertical-align:-0.23em;",[568,2796,2798],{"className":2797},[621,2408],[568,2799,2801,2863],{"className":2800},[683,684],[568,2802,2804,2860],{"className":2803},[688],[568,2805,2808,2843],{"className":2806,"style":2807},[692],"height:0.81em;",[568,2809,2812,2815],{"className":2810,"style":2811},[2422],"top:-3em;",[568,2813],{"className":2814,"style":1241},[700],[568,2816,2819,2822,2825,2828,2831,2834,2840],{"className":2817,"style":2818},[621],"padding-left:0.833em;",[568,2820,2568],{"className":2821},[621],[568,2823],{"className":2824,"style":1169},[625],[568,2826,1678],{"className":2827},[1173],[568,2829],{"className":2830,"style":1169},[625],[568,2832,1432],{"className":2833},[621],[568,2835,2837],{"className":2836},[621],[568,2838,1440],{"className":2839},[1439],[568,2841,1544],{"className":2842},[621],[568,2844,2846,2849],{"style":2845},"top:-2.77em;",[568,2847],{"className":2848,"style":1241},[700],[568,2850,2853],{"className":2851,"style":2852},[2527],"min-width:0.853em;height:1.08em;",[2530,2854,2857],{"xmlns":2532,"width":2533,"height":2855,"viewBox":2856,"preserveAspectRatio":2536},"1.08em","0 0 400000 1080",[2538,2858],{"d":2859},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[568,2861,716],{"className":2862},[715],[568,2864,2866],{"className":2865},[688],[568,2867,2870],{"className":2868,"style":2869},[692],"height:0.23em;",[568,2871],{},[568,2873],{"className":2874,"style":959},[625],[568,2876,1394],{"className":2877},[963],[568,2879],{"className":2880,"style":959},[625],[568,2882,2884,2887],{"className":2883},[612],[568,2885],{"className":2886,"style":1003},[616],[568,2888,1444],{"className":2889},[621]," auf ",[568,2892,2894,2924],{"className":2893},[571],[568,2895,2897],{"className":2896},[575],[577,2898,2899],{"xmlns":579},[581,2900,2901,2921],{},[584,2902,2903,2917,2919],{},[2372,2904,2905],{},[584,2906,2907,2909,2911,2913,2915],{},[587,2908,2113],{},[591,2910,593],{},[587,2912,2118],{},[935,2914,1678],{},[587,2916,1474],{},[935,2918,1394],{},[587,2920,589],{},[600,2922,2923],{"encoding":602},"\\sqrt{10\\,000 \\cdot 0{,}25} = 50",[568,2925,2927,3016],{"className":2926,"ariaHidden":608},[607],[568,2928,2930,2933,3007,3010,3013],{"className":2929},[612],[568,2931],{"className":2932,"style":2794},[616],[568,2934,2936],{"className":2935},[621,2408],[568,2937,2939,2999],{"className":2938},[683,684],[568,2940,2942,2996],{"className":2941},[688],[568,2943,2945,2984],{"className":2944,"style":2807},[692],[568,2946,2948,2951],{"className":2947,"style":2811},[2422],[568,2949],{"className":2950,"style":1241},[700],[568,2952,2954,2957,2960,2963,2966,2969,2972,2975,2981],{"className":2953,"style":2818},[621],[568,2955,2113],{"className":2956},[621],[568,2958],{"className":2959,"style":626},[625],[568,2961,2118],{"className":2962},[621],[568,2964],{"className":2965,"style":1169},[625],[568,2967,1678],{"className":2968},[1173],[568,2970],{"className":2971,"style":1169},[625],[568,2973,1432],{"className":2974},[621],[568,2976,2978],{"className":2977},[621],[568,2979,1440],{"className":2980},[1439],[568,2982,1544],{"className":2983},[621],[568,2985,2986,2989],{"style":2845},[568,2987],{"className":2988,"style":1241},[700],[568,2990,2992],{"className":2991,"style":2852},[2527],[2530,2993,2994],{"xmlns":2532,"width":2533,"height":2855,"viewBox":2856,"preserveAspectRatio":2536},[2538,2995],{"d":2859},[568,2997,716],{"className":2998},[715],[568,3000,3002],{"className":3001},[688],[568,3003,3005],{"className":3004,"style":2869},[692],[568,3006],{},[568,3008],{"className":3009,"style":959},[625],[568,3011,1394],{"className":3012},[963],[568,3014],{"className":3015,"style":959},[625],[568,3017,3019,3022],{"className":3018},[612],[568,3020],{"className":3021,"style":1003},[616],[568,3023,589],{"className":3024},[621],". Nur der ",[632,3027,3028],{},"Anteil"," nähert sich ",[568,3031,3033,3046],{"className":3032},[571],[568,3034,3036],{"className":3035},[575],[577,3037,3038],{"xmlns":579},[581,3039,3040,3044],{},[584,3041,3042],{},[595,3043,564],{},[600,3045,564],{"encoding":602},[568,3047,3049],{"className":3048,"ariaHidden":608},[607],[568,3050,3052,3055],{"className":3051},[612],[568,3053],{"className":3054,"style":752},[616],[568,3056,564],{"className":3057},[621,675],[2709,3059,3060,3061,3089],{},"Das Gesetz als Garantie für eine bestimmte Versuchsreihe lesen. Es sagt nur, dass große Abweichungen der relativen Häufigkeit von ",[568,3062,3064,3077],{"className":3063},[571],[568,3065,3067],{"className":3066},[575],[577,3068,3069],{"xmlns":579},[581,3070,3071,3075],{},[584,3072,3073],{},[595,3074,564],{},[600,3076,564],{"encoding":602},[568,3078,3080],{"className":3079,"ariaHidden":608},[607],[568,3081,3083,3086],{"className":3082},[612],[568,3084],{"className":3085,"style":752},[616],[568,3087,564],{"className":3088},[621,675]," immer unwahrscheinlicher werden.",{"title":3091,"searchDepth":3092,"depth":3092,"links":3093},"",2,[3094,3095,3096],{"id":561,"depth":3092,"text":562},{"id":1343,"depth":3092,"text":1344},{"id":2703,"depth":3092,"text":2704},[3098,3101,3104,3107,3110,3113,3115],{"lhs":3099,"rhs":3100},"0.25 \u002F (1000 * 0.05^2)","0.1",{"lhs":3102,"rhs":3103},"1 - 0.25 \u002F (1000 * 0.05^2)","0.9",{"lhs":3105,"rhs":3106},"0.25 \u002F (10000 * 0.05^2)","0.01",{"lhs":3108,"rhs":3109},"sqrt(0.5 * 0.5 \u002F 100)","0.05",{"lhs":3111,"rhs":3112},"sqrt(0.5 * 0.5 \u002F 10000)","0.005",{"lhs":3114,"rhs":1444},"sqrt(100 * 0.5 * 0.5)",{"lhs":3116,"rhs":589},"sqrt(10000 * 0.5 * 0.5)","n \\text{ unabhängige Versuche mit gleicher Trefferwahrscheinlichkeit } p,\\ \\varepsilon > 0","\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> \u003Cspan class=\"katex\">unabhängige Versuche mit gleicher Trefferwahrscheinlichkeit\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\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>\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>ε\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\varepsilon > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">ε\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","law-of-large-numbers","\\lim_{n \\to \\infty} P\\left(|h_n - p| \u003C \\varepsilon\\right) = 1","\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>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmi>P\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>h\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>ε\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lim_{n \\to \\infty} P\\left(|h_n - p| < \\varepsilon\\right) = 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:1.45em;vertical-align:-0.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\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:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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>\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:0.2222em;\">\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=\"mord\">∣\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=\"mord mathnormal\">ε\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgesetz-der-grossen-zahlen",[],[3130,3131,3132,3133],"relative-frequency","chebyshev-inequality","binomial-mean-sd","laplace-probability",{"title":548,"description":3091},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgesetz-der-grossen-zahlen","Mit wachsender 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