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Deshalb zieht man ",[568,748,750,775],{"className":749},[571],[568,751,753],{"className":752},[575],[577,754,755],{"xmlns":579},[581,756,757,772],{},[584,758,759,761,763,765,768,770],{},[587,760,666],{},[591,762,670],{"stretchy":669},[587,764,589],{},[591,766,767],{},"∩",[587,769,596],{},[591,771,675],{"stretchy":669},[598,773,774],{"encoding":600},"P(A \\cap B)",[568,776,778,802],{"className":777,"ariaHidden":606},[605],[568,779,781,784,787,790,793,796,799],{"className":780},[610],[568,782],{"className":783,"style":699},[614],[568,785,666],{"className":786,"style":703},[619,620],[568,788,670],{"className":789},[707],[568,791,589],{"className":792},[619,620],[568,794],{"className":795,"style":625},[624],[568,797,767],{"className":798},[629],[568,800],{"className":801,"style":625},[624],[568,803,805,808,811],{"className":804},[610],[568,806],{"className":807,"style":699},[614],[568,809,596],{"className":810,"style":642},[619,620],[568,812,675],{"className":813},[714]," einmal ab. Im Mengenbild (Venn-Diagramm) ist das die Überlappung der beiden Kreise.",[564,816,817,818,846,847,875,876,879,880,974,975,1115],{},"Sonderfall: Können ",[568,819,821,834],{"className":820},[571],[568,822,824],{"className":823},[575],[577,825,826],{"xmlns":579},[581,827,828,832],{},[584,829,830],{},[587,831,589],{},[598,833,589],{"encoding":600},[568,835,837],{"className":836,"ariaHidden":606},[605],[568,838,840,843],{"className":839},[610],[568,841],{"className":842,"style":615},[614],[568,844,589],{"className":845},[619,620]," und ",[568,848,850,863],{"className":849},[571],[568,851,853],{"className":852},[575],[577,854,855],{"xmlns":579},[581,856,857,861],{},[584,858,859],{},[587,860,596],{},[598,862,596],{"encoding":600},[568,864,866],{"className":865,"ariaHidden":606},[605],[568,867,869,872],{"className":868},[610],[568,870],{"className":871,"style":615},[614],[568,873,596],{"className":874,"style":642},[619,620]," nicht gleichzeitig eintreten (",[645,877,878],{},"unvereinbare"," Ereignisse), ist ",[568,881,883,914],{"className":882},[571],[568,884,886],{"className":885},[575],[577,887,888],{"xmlns":579},[581,889,890,911],{},[584,891,892,894,896,898,900,902,904,907],{},[587,893,666],{},[591,895,670],{"stretchy":669},[587,897,589],{},[591,899,767],{},[587,901,596],{},[591,903,675],{"stretchy":669},[591,905,906],{},"=",[908,909,910],"mn",{},"0",[598,912,913],{"encoding":600},"P(A \\cap B) = 0",[568,915,917,941,964],{"className":916,"ariaHidden":606},[605],[568,918,920,923,926,929,932,935,938],{"className":919},[610],[568,921],{"className":922,"style":699},[614],[568,924,666],{"className":925,"style":703},[619,620],[568,927,670],{"className":928},[707],[568,930,589],{"className":931},[619,620],[568,933],{"className":934,"style":625},[624],[568,936,767],{"className":937},[629],[568,939],{"className":940,"style":625},[624],[568,942,944,947,950,953,957,961],{"className":943},[610],[568,945],{"className":946,"style":699},[614],[568,948,596],{"className":949,"style":642},[619,620],[568,951,675],{"className":952},[714],[568,954],{"className":955,"style":956},[624],"margin-right:0.2778em;",[568,958,906],{"className":959},[960],"mrel",[568,962],{"className":963,"style":956},[624],[568,965,967,971],{"className":966},[610],[568,968],{"className":969,"style":970},[614],"height:0.6444em;",[568,972,910],{"className":973},[619]," und es gilt einfach ",[568,976,978,1022],{"className":977},[571],[568,979,981],{"className":980},[575],[577,982,983],{"xmlns":579},[581,984,985,1019],{},[584,986,987,989,991,993,995,997,999,1001,1003,1005,1007,1009,1011,1013,1015,1017],{},[587,988,666],{},[591,990,670],{"stretchy":669},[587,992,589],{},[591,994,593],{},[587,996,596],{},[591,998,675],{"stretchy":669},[591,1000,906],{},[587,1002,666],{},[591,1004,670],{"stretchy":669},[587,1006,589],{},[591,1008,675],{"stretchy":669},[591,1010,678],{},[587,1012,666],{},[591,1014,670],{"stretchy":669},[587,1016,596],{},[591,1018,675],{"stretchy":669},[598,1020,1021],{"encoding":600},"P(A \\cup B) = P(A) + P(B)",[568,1023,1025,1049,1070,1097],{"className":1024,"ariaHidden":606},[605],[568,1026,1028,1031,1034,1037,1040,1043,1046],{"className":1027},[610],[568,1029],{"className":1030,"style":699},[614],[568,1032,666],{"className":1033,"style":703},[619,620],[568,1035,670],{"className":1036},[707],[568,1038,589],{"className":1039},[619,620],[568,1041],{"className":1042,"style":625},[624],[568,1044,593],{"className":1045},[629],[568,1047],{"className":1048,"style":625},[624],[568,1050,1052,1055,1058,1061,1064,1067],{"className":1051},[610],[568,1053],{"className":1054,"style":699},[614],[568,1056,596],{"className":1057,"style":642},[619,620],[568,1059,675],{"className":1060},[714],[568,1062],{"className":1063,"style":956},[624],[568,1065,906],{"className":1066},[960],[568,1068],{"className":1069,"style":956},[624],[568,1071,1073,1076,1079,1082,1085,1088,1091,1094],{"className":1072},[610],[568,1074],{"className":1075,"style":699},[614],[568,1077,666],{"className":1078,"style":703},[619,620],[568,1080,670],{"className":1081},[707],[568,1083,589],{"className":1084},[619,620],[568,1086,675],{"className":1087},[714],[568,1089],{"className":1090,"style":625},[624],[568,1092,678],{"className":1093},[629],[568,1095],{"className":1096,"style":625},[624],[568,1098,1100,1103,1106,1109,1112],{"className":1099},[610],[568,1101],{"className":1102,"style":699},[614],[568,1104,666],{"className":1105,"style":703},[619,620],[568,1107,670],{"className":1108},[707],[568,1110,596],{"className":1111,"style":642},[619,620],[568,1113,675],{"className":1114},[714],".",[559,1117,1119],{"id":1118},"beispiele","Beispiele",[564,1121,1122,1123,1151,1152,1240,1241,1269,1270,1350,1351,1403],{},"Ein Würfel wird geworfen. ",[568,1124,1126,1139],{"className":1125},[571],[568,1127,1129],{"className":1128},[575],[577,1130,1131],{"xmlns":579},[581,1132,1133,1137],{},[584,1134,1135],{},[587,1136,589],{},[598,1138,589],{"encoding":600},[568,1140,1142],{"className":1141,"ariaHidden":606},[605],[568,1143,1145,1148],{"className":1144},[610],[568,1146],{"className":1147,"style":615},[614],[568,1149,589],{"className":1150},[619,620],": „gerade Zahl“ ",[568,1153,1155,1189],{"className":1154},[571],[568,1156,1158],{"className":1157},[575],[577,1159,1160],{"xmlns":579},[581,1161,1162,1186],{},[584,1163,1164,1166,1169,1172,1175,1178,1180,1183],{},[591,1165,906],{},[591,1167,1168],{"stretchy":669},"{",[908,1170,1171],{},"2",[591,1173,1174],{"separator":606},",",[908,1176,1177],{},"4",[591,1179,1174],{"separator":606},[908,1181,1182],{},"6",[591,1184,1185],{"stretchy":669},"}",[598,1187,1188],{"encoding":600},"= \\{2, 4, 6\\}",[568,1190,1192,1205],{"className":1191,"ariaHidden":606},[605],[568,1193,1195,1199,1202],{"className":1194},[610],[568,1196],{"className":1197,"style":1198},[614],"height:0.3669em;",[568,1200,906],{"className":1201},[960],[568,1203],{"className":1204,"style":956},[624],[568,1206,1208,1211,1214,1217,1221,1225,1228,1231,1234,1237],{"className":1207},[610],[568,1209],{"className":1210,"style":699},[614],[568,1212,1168],{"className":1213},[707],[568,1215,1171],{"className":1216},[619],[568,1218,1174],{"className":1219},[1220],"mpunct",[568,1222],{"className":1223,"style":1224},[624],"margin-right:0.1667em;",[568,1226,1177],{"className":1227},[619],[568,1229,1174],{"className":1230},[1220],[568,1232],{"className":1233,"style":1224},[624],[568,1235,1182],{"className":1236},[619],[568,1238,1185],{"className":1239},[714],", ",[568,1242,1244,1257],{"className":1243},[571],[568,1245,1247],{"className":1246},[575],[577,1248,1249],{"xmlns":579},[581,1250,1251,1255],{},[584,1252,1253],{},[587,1254,596],{},[598,1256,596],{"encoding":600},[568,1258,1260],{"className":1259,"ariaHidden":606},[605],[568,1261,1263,1266],{"className":1262},[610],[568,1264],{"className":1265,"style":615},[614],[568,1267,596],{"className":1268,"style":642},[619,620],": „größer als 3“ ",[568,1271,1273,1302],{"className":1272},[571],[568,1274,1276],{"className":1275},[575],[577,1277,1278],{"xmlns":579},[581,1279,1280,1299],{},[584,1281,1282,1284,1286,1288,1290,1293,1295,1297],{},[591,1283,906],{},[591,1285,1168],{"stretchy":669},[908,1287,1177],{},[591,1289,1174],{"separator":606},[908,1291,1292],{},"5",[591,1294,1174],{"separator":606},[908,1296,1182],{},[591,1298,1185],{"stretchy":669},[598,1300,1301],{"encoding":600},"= \\{4, 5, 6\\}",[568,1303,1305,1317],{"className":1304,"ariaHidden":606},[605],[568,1306,1308,1311,1314],{"className":1307},[610],[568,1309],{"className":1310,"style":1198},[614],[568,1312,906],{"className":1313},[960],[568,1315],{"className":1316,"style":956},[624],[568,1318,1320,1323,1326,1329,1332,1335,1338,1341,1344,1347],{"className":1319},[610],[568,1321],{"className":1322,"style":699},[614],[568,1324,1168],{"className":1325},[707],[568,1327,1177],{"className":1328},[619],[568,1330,1174],{"className":1331},[1220],[568,1333],{"className":1334,"style":1224},[624],[568,1336,1292],{"className":1337},[619],[568,1339,1174],{"className":1340},[1220],[568,1342],{"className":1343,"style":1224},[624],[568,1345,1182],{"className":1346},[619],[568,1348,1185],{"className":1349},[714],". Beide treffen auf ",[568,1352,1354,1376],{"className":1353},[571],[568,1355,1357],{"className":1356},[575],[577,1358,1359],{"xmlns":579},[581,1360,1361,1373],{},[584,1362,1363,1365,1367,1369,1371],{},[591,1364,1168],{"stretchy":669},[908,1366,1177],{},[591,1368,1174],{"separator":606},[908,1370,1182],{},[591,1372,1185],{"stretchy":669},[598,1374,1375],{"encoding":600},"\\{4, 6\\}",[568,1377,1379],{"className":1378,"ariaHidden":606},[605],[568,1380,1382,1385,1388,1391,1394,1397,1400],{"className":1381},[610],[568,1383],{"className":1384,"style":699},[614],[568,1386,1168],{"className":1387},[707],[568,1389,1177],{"className":1390},[619],[568,1392,1174],{"className":1393},[1220],[568,1395],{"className":1396,"style":1224},[624],[568,1398,1182],{"className":1399},[619],[568,1401,1185],{"className":1402},[714]," zu:",[568,1405,1408],{"className":1406},[1407],"katex-display",[568,1409,1411,1479],{"className":1410},[571],[568,1412,1414],{"className":1413},[575],[577,1415,1417],{"xmlns":579,"display":1416},"block",[581,1418,1419,1476],{},[584,1420,1421,1423,1425,1427,1429,1431,1433,1435,1443,1445,1451,1454,1460,1462,1468,1470],{},[587,1422,666],{},[591,1424,670],{"stretchy":669},[587,1426,589],{},[591,1428,593],{},[587,1430,596],{},[591,1432,675],{"stretchy":669},[591,1434,906],{},[1436,1437,1438,1441],"mfrac",{},[908,1439,1440],{},"3",[908,1442,1182],{},[591,1444,678],{},[1436,1446,1447,1449],{},[908,1448,1440],{},[908,1450,1182],{},[591,1452,1453],{},"−",[1436,1455,1456,1458],{},[908,1457,1171],{},[908,1459,1182],{},[591,1461,906],{},[1436,1463,1464,1466],{},[908,1465,1177],{},[908,1467,1182],{},[591,1469,906],{},[1436,1471,1472,1474],{},[908,1473,1171],{},[908,1475,1440],{},[598,1477,1478],{"encoding":600},"P(A \\cup B) = \\frac{3}{6} + \\frac{3}{6} - \\frac{2}{6} = \\frac{4}{6} = \\frac{2}{3}",[568,1480,1482,1506,1527,1621,1698,1775,1852],{"className":1481,"ariaHidden":606},[605],[568,1483,1485,1488,1491,1494,1497,1500,1503],{"className":1484},[610],[568,1486],{"className":1487,"style":699},[614],[568,1489,666],{"className":1490,"style":703},[619,620],[568,1492,670],{"className":1493},[707],[568,1495,589],{"className":1496},[619,620],[568,1498],{"className":1499,"style":625},[624],[568,1501,593],{"className":1502},[629],[568,1504],{"className":1505,"style":625},[624],[568,1507,1509,1512,1515,1518,1521,1524],{"className":1508},[610],[568,1510],{"className":1511,"style":699},[614],[568,1513,596],{"className":1514,"style":642},[619,620],[568,1516,675],{"className":1517},[714],[568,1519],{"className":1520,"style":956},[624],[568,1522,906],{"className":1523},[960],[568,1525],{"className":1526,"style":956},[624],[568,1528,1530,1534,1612,1615,1618],{"className":1529},[610],[568,1531],{"className":1532,"style":1533},[614],"height:2.0074em;vertical-align:-0.686em;",[568,1535,1537,1541,1609],{"className":1536},[619],[568,1538],{"className":1539},[707,1540],"nulldelimiter",[568,1542,1544],{"className":1543},[1436],[568,1545,1549,1600],{"className":1546},[1547,1548],"vlist-t","vlist-t2",[568,1550,1553,1595],{"className":1551},[1552],"vlist-r",[568,1554,1558,1572,1583],{"className":1555,"style":1557},[1556],"vlist","height:1.3214em;",[568,1559,1561,1566],{"style":1560},"top:-2.314em;",[568,1562],{"className":1563,"style":1565},[1564],"pstrut","height:3em;",[568,1567,1569],{"className":1568},[619],[568,1570,1182],{"className":1571},[619],[568,1573,1575,1578],{"style":1574},"top:-3.23em;",[568,1576],{"className":1577,"style":1565},[1564],[568,1579],{"className":1580,"style":1582},[1581],"frac-line","border-bottom-width:0.04em;",[568,1584,1586,1589],{"style":1585},"top:-3.677em;",[568,1587],{"className":1588,"style":1565},[1564],[568,1590,1592],{"className":1591},[619],[568,1593,1440],{"className":1594},[619],[568,1596,1599],{"className":1597},[1598],"vlist-s","​",[568,1601,1603],{"className":1602},[1552],[568,1604,1607],{"className":1605,"style":1606},[1556],"height:0.686em;",[568,1608],{},[568,1610],{"className":1611},[714,1540],[568,1613],{"className":1614,"style":625},[624],[568,1616,678],{"className":1617},[629],[568,1619],{"className":1620,"style":625},[624],[568,1622,1624,1627,1689,1692,1695],{"className":1623},[610],[568,1625],{"className":1626,"style":1533},[614],[568,1628,1630,1633,1686],{"className":1629},[619],[568,1631],{"className":1632},[707,1540],[568,1634,1636],{"className":1635},[1436],[568,1637,1639,1678],{"className":1638},[1547,1548],[568,1640,1642,1675],{"className":1641},[1552],[568,1643,1645,1656,1664],{"className":1644,"style":1557},[1556],[568,1646,1647,1650],{"style":1560},[568,1648],{"className":1649,"style":1565},[1564],[568,1651,1653],{"className":1652},[619],[568,1654,1182],{"className":1655},[619],[568,1657,1658,1661],{"style":1574},[568,1659],{"className":1660,"style":1565},[1564],[568,1662],{"className":1663,"style":1582},[1581],[568,1665,1666,1669],{"style":1585},[568,1667],{"className":1668,"style":1565},[1564],[568,1670,1672],{"className":1671},[619],[568,1673,1440],{"className":1674},[619],[568,1676,1599],{"className":1677},[1598],[568,1679,1681],{"className":1680},[1552],[568,1682,1684],{"className":1683,"style":1606},[1556],[568,1685],{},[568,1687],{"className":1688},[714,1540],[568,1690],{"className":1691,"style":625},[624],[568,1693,1453],{"className":1694},[629],[568,1696],{"className":1697,"style":625},[624],[568,1699,1701,1704,1766,1769,1772],{"className":1700},[610],[568,1702],{"className":1703,"style":1533},[614],[568,1705,1707,1710,1763],{"className":1706},[619],[568,1708],{"className":1709},[707,1540],[568,1711,1713],{"className":1712},[1436],[568,1714,1716,1755],{"className":1715},[1547,1548],[568,1717,1719,1752],{"className":1718},[1552],[568,1720,1722,1733,1741],{"className":1721,"style":1557},[1556],[568,1723,1724,1727],{"style":1560},[568,1725],{"className":1726,"style":1565},[1564],[568,1728,1730],{"className":1729},[619],[568,1731,1182],{"className":1732},[619],[568,1734,1735,1738],{"style":1574},[568,1736],{"className":1737,"style":1565},[1564],[568,1739],{"className":1740,"style":1582},[1581],[568,1742,1743,1746],{"style":1585},[568,1744],{"className":1745,"style":1565},[1564],[568,1747,1749],{"className":1748},[619],[568,1750,1171],{"className":1751},[619],[568,1753,1599],{"className":1754},[1598],[568,1756,1758],{"className":1757},[1552],[568,1759,1761],{"className":1760,"style":1606},[1556],[568,1762],{},[568,1764],{"className":1765},[714,1540],[568,1767],{"className":1768,"style":956},[624],[568,1770,906],{"className":1771},[960],[568,1773],{"className":1774,"style":956},[624],[568,1776,1778,1781,1843,1846,1849],{"className":1777},[610],[568,1779],{"className":1780,"style":1533},[614],[568,1782,1784,1787,1840],{"className":1783},[619],[568,1785],{"className":1786},[707,1540],[568,1788,1790],{"className":1789},[1436],[568,1791,1793,1832],{"className":1792},[1547,1548],[568,1794,1796,1829],{"className":1795},[1552],[568,1797,1799,1810,1818],{"className":1798,"style":1557},[1556],[568,1800,1801,1804],{"style":1560},[568,1802],{"className":1803,"style":1565},[1564],[568,1805,1807],{"className":1806},[619],[568,1808,1182],{"className":1809},[619],[568,1811,1812,1815],{"style":1574},[568,1813],{"className":1814,"style":1565},[1564],[568,1816],{"className":1817,"style":1582},[1581],[568,1819,1820,1823],{"style":1585},[568,1821],{"className":1822,"style":1565},[1564],[568,1824,1826],{"className":1825},[619],[568,1827,1177],{"className":1828},[619],[568,1830,1599],{"className":1831},[1598],[568,1833,1835],{"className":1834},[1552],[568,1836,1838],{"className":1837,"style":1606},[1556],[568,1839],{},[568,1841],{"className":1842},[714,1540],[568,1844],{"className":1845,"style":956},[624],[568,1847,906],{"className":1848},[960],[568,1850],{"className":1851,"style":956},[624],[568,1853,1855,1858],{"className":1854},[610],[568,1856],{"className":1857,"style":1533},[614],[568,1859,1861,1864,1917],{"className":1860},[619],[568,1862],{"className":1863},[707,1540],[568,1865,1867],{"className":1866},[1436],[568,1868,1870,1909],{"className":1869},[1547,1548],[568,1871,1873,1906],{"className":1872},[1552],[568,1874,1876,1887,1895],{"className":1875,"style":1557},[1556],[568,1877,1878,1881],{"style":1560},[568,1879],{"className":1880,"style":1565},[1564],[568,1882,1884],{"className":1883},[619],[568,1885,1440],{"className":1886},[619],[568,1888,1889,1892],{"style":1574},[568,1890],{"className":1891,"style":1565},[1564],[568,1893],{"className":1894,"style":1582},[1581],[568,1896,1897,1900],{"style":1585},[568,1898],{"className":1899,"style":1565},[1564],[568,1901,1903],{"className":1902},[619],[568,1904,1171],{"className":1905},[619],[568,1907,1599],{"className":1908},[1598],[568,1910,1912],{"className":1911},[1552],[568,1913,1915],{"className":1914,"style":1606},[1556],[568,1916],{},[568,1918],{"className":1919},[714,1540],[564,1921,1922,1923,2045,2046,2074],{},"Zur Kontrolle: ",[568,1924,1926,1964],{"className":1925},[571],[568,1927,1929],{"className":1928},[575],[577,1930,1931],{"xmlns":579},[581,1932,1933,1961],{},[584,1934,1935,1937,1939,1941,1943,1945,1947,1949,1951,1953,1955,1957,1959],{},[587,1936,589],{},[591,1938,593],{},[587,1940,596],{},[591,1942,906],{},[591,1944,1168],{"stretchy":669},[908,1946,1171],{},[591,1948,1174],{"separator":606},[908,1950,1177],{},[591,1952,1174],{"separator":606},[908,1954,1292],{},[591,1956,1174],{"separator":606},[908,1958,1182],{},[591,1960,1185],{"stretchy":669},[598,1962,1963],{"encoding":600},"A \\cup B = \\{2, 4, 5, 6\\}",[568,1965,1967,1985,2003],{"className":1966,"ariaHidden":606},[605],[568,1968,1970,1973,1976,1979,1982],{"className":1969},[610],[568,1971],{"className":1972,"style":615},[614],[568,1974,589],{"className":1975},[619,620],[568,1977],{"className":1978,"style":625},[624],[568,1980,593],{"className":1981},[629],[568,1983],{"className":1984,"style":625},[624],[568,1986,1988,1991,1994,1997,2000],{"className":1987},[610],[568,1989],{"className":1990,"style":615},[614],[568,1992,596],{"className":1993,"style":642},[619,620],[568,1995],{"className":1996,"style":956},[624],[568,1998,906],{"className":1999},[960],[568,2001],{"className":2002,"style":956},[624],[568,2004,2006,2009,2012,2015,2018,2021,2024,2027,2030,2033,2036,2039,2042],{"className":2005},[610],[568,2007],{"className":2008,"style":699},[614],[568,2010,1168],{"className":2011},[707],[568,2013,1171],{"className":2014},[619],[568,2016,1174],{"className":2017},[1220],[568,2019],{"className":2020,"style":1224},[624],[568,2022,1177],{"className":2023},[619],[568,2025,1174],{"className":2026},[1220],[568,2028],{"className":2029,"style":1224},[624],[568,2031,1292],{"className":2032},[619],[568,2034,1174],{"className":2035},[1220],[568,2037],{"className":2038,"style":1224},[624],[568,2040,1182],{"className":2041},[619],[568,2043,1185],{"className":2044},[714]," hat tatsächlich ",[568,2047,2049,2062],{"className":2048},[571],[568,2050,2052],{"className":2051},[575],[577,2053,2054],{"xmlns":579},[581,2055,2056,2060],{},[584,2057,2058],{},[908,2059,1177],{},[598,2061,1177],{"encoding":600},[568,2063,2065],{"className":2064,"ariaHidden":606},[605],[568,2066,2068,2071],{"className":2067},[610],[568,2069],{"className":2070,"style":970},[614],[568,2072,1177],{"className":2073},[619]," Elemente.",[564,2076,2077],{},"In einer Jahrgangsstufe spielen 40 % ein Instrument, 55 % treiben Sport im Verein und 20 % machen beides. Für eine zufällig ausgewählte Person gilt:",[568,2079,2081],{"className":2080},[1407],[568,2082,2084,2126],{"className":2083},[571],[568,2085,2087],{"className":2086},[575],[577,2088,2089],{"xmlns":579,"display":1416},[581,2090,2091,2123],{},[584,2092,2093,2095,2097,2101,2103,2105,2108,2110,2113,2115,2118,2120],{},[587,2094,666],{},[591,2096,670],{"stretchy":669},[2098,2099,2100],"mtext",{},"Instrument oder Verein",[591,2102,675],{"stretchy":669},[591,2104,906],{},[908,2106,2107],{},"0,40",[591,2109,678],{},[908,2111,2112],{},"0,55",[591,2114,1453],{},[908,2116,2117],{},"0,20",[591,2119,906],{},[908,2121,2122],{},"0,75",[598,2124,2125],{"encoding":600},"P(\\text{Instrument oder Verein}) = 0{,}40 + 0{,}55 - 0{,}20 = 0{,}75",[568,2127,2129,2160,2189,2217,2245],{"className":2128,"ariaHidden":606},[605],[568,2130,2132,2135,2138,2141,2148,2151,2154,2157],{"className":2131},[610],[568,2133],{"className":2134,"style":699},[614],[568,2136,666],{"className":2137,"style":703},[619,620],[568,2139,670],{"className":2140},[707],[568,2142,2145],{"className":2143},[619,2144],"text",[568,2146,2100],{"className":2147},[619],[568,2149,675],{"className":2150},[714],[568,2152],{"className":2153,"style":956},[624],[568,2155,906],{"className":2156},[960],[568,2158],{"className":2159,"style":956},[624],[568,2161,2163,2167,2170,2176,2180,2183,2186],{"className":2162},[610],[568,2164],{"className":2165,"style":2166},[614],"height:0.8389em;vertical-align:-0.1944em;",[568,2168,910],{"className":2169},[619],[568,2171,2173],{"className":2172},[619],[568,2174,1174],{"className":2175},[1220],[568,2177,2179],{"className":2178},[619],"40",[568,2181],{"className":2182,"style":625},[624],[568,2184,678],{"className":2185},[629],[568,2187],{"className":2188,"style":625},[624],[568,2190,2192,2195,2198,2204,2208,2211,2214],{"className":2191},[610],[568,2193],{"className":2194,"style":2166},[614],[568,2196,910],{"className":2197},[619],[568,2199,2201],{"className":2200},[619],[568,2202,1174],{"className":2203},[1220],[568,2205,2207],{"className":2206},[619],"55",[568,2209],{"className":2210,"style":625},[624],[568,2212,1453],{"className":2213},[629],[568,2215],{"className":2216,"style":625},[624],[568,2218,2220,2223,2226,2232,2236,2239,2242],{"className":2219},[610],[568,2221],{"className":2222,"style":2166},[614],[568,2224,910],{"className":2225},[619],[568,2227,2229],{"className":2228},[619],[568,2230,1174],{"className":2231},[1220],[568,2233,2235],{"className":2234},[619],"20",[568,2237],{"className":2238,"style":956},[624],[568,2240,906],{"className":2241},[960],[568,2243],{"className":2244,"style":956},[624],[568,2246,2248,2251,2254,2260],{"className":2247},[610],[568,2249],{"className":2250,"style":2166},[614],[568,2252,910],{"className":2253},[619],[568,2255,2257],{"className":2256},[619],[568,2258,1174],{"className":2259},[1220],[568,2261,2263],{"className":2262},[619],"75",[564,2265,2266],{},"Mit der Gegenwahrscheinlichkeit folgt: 25 % machen keines von beiden.",[559,2268,2270],{"id":2269},"typische-fehler","Typische Fehler",[2272,2273,2274,2475,2611,3298],"ul",{},[2275,2276,2277,2342,2343,2445,2446,1115],"li",{},[568,2278,2280,2303],{"className":2279},[571],[568,2281,2283],{"className":2282},[575],[577,2284,2285],{"xmlns":579},[581,2286,2287,2301],{},[584,2288,2289,2291,2293,2295,2297,2299],{},[587,2290,666],{},[591,2292,670],{"stretchy":669},[587,2294,589],{},[591,2296,767],{},[587,2298,596],{},[591,2300,675],{"stretchy":669},[598,2302,774],{"encoding":600},[568,2304,2306,2330],{"className":2305,"ariaHidden":606},[605],[568,2307,2309,2312,2315,2318,2321,2324,2327],{"className":2308},[610],[568,2310],{"className":2311,"style":699},[614],[568,2313,666],{"className":2314,"style":703},[619,620],[568,2316,670],{"className":2317},[707],[568,2319,589],{"className":2320},[619,620],[568,2322],{"className":2323,"style":625},[624],[568,2325,767],{"className":2326},[629],[568,2328],{"className":2329,"style":625},[624],[568,2331,2333,2336,2339],{"className":2332},[610],[568,2334],{"className":2335,"style":699},[614],[568,2337,596],{"className":2338,"style":642},[619,620],[568,2340,675],{"className":2341},[714]," vergessen. Im Beispiel käme ",[568,2344,2346,2369],{"className":2345},[571],[568,2347,2349],{"className":2348},[575],[577,2350,2351],{"xmlns":579},[581,2352,2353,2366],{},[584,2354,2355,2357,2359,2361,2363],{},[908,2356,2107],{},[591,2358,678],{},[908,2360,2112],{},[591,2362,906],{},[908,2364,2365],{},"0,95",[598,2367,2368],{"encoding":600},"0{,}40 + 0{,}55 = 0{,}95",[568,2370,2372,2399,2426],{"className":2371,"ariaHidden":606},[605],[568,2373,2375,2378,2381,2387,2390,2393,2396],{"className":2374},[610],[568,2376],{"className":2377,"style":2166},[614],[568,2379,910],{"className":2380},[619],[568,2382,2384],{"className":2383},[619],[568,2385,1174],{"className":2386},[1220],[568,2388,2179],{"className":2389},[619],[568,2391],{"className":2392,"style":625},[624],[568,2394,678],{"className":2395},[629],[568,2397],{"className":2398,"style":625},[624],[568,2400,2402,2405,2408,2414,2417,2420,2423],{"className":2401},[610],[568,2403],{"className":2404,"style":2166},[614],[568,2406,910],{"className":2407},[619],[568,2409,2411],{"className":2410},[619],[568,2412,1174],{"className":2413},[1220],[568,2415,2207],{"className":2416},[619],[568,2418],{"className":2419,"style":956},[624],[568,2421,906],{"className":2422},[960],[568,2424],{"className":2425,"style":956},[624],[568,2427,2429,2432,2435,2441],{"className":2428},[610],[568,2430],{"className":2431,"style":2166},[614],[568,2433,910],{"className":2434},[619],[568,2436,2438],{"className":2437},[619],[568,2439,1174],{"className":2440},[1220],[568,2442,2444],{"className":2443},[619],"95"," heraus, bei anderen Zahlen sogar mehr als ",[568,2447,2449,2463],{"className":2448},[571],[568,2450,2452],{"className":2451},[575],[577,2453,2454],{"xmlns":579},[581,2455,2456,2461],{},[584,2457,2458],{},[908,2459,2460],{},"1",[598,2462,2460],{"encoding":600},[568,2464,2466],{"className":2465,"ariaHidden":606},[605],[568,2467,2469,2472],{"className":2468},[610],[568,2470],{"className":2471,"style":970},[614],[568,2473,2460],{"className":2474},[619],[2275,2476,2477,2478,2544,2545,2610],{},"„Oder“ als „entweder … oder“ lesen. ",[568,2479,2481,2505],{"className":2480},[571],[568,2482,2484],{"className":2483},[575],[577,2485,2486],{"xmlns":579},[581,2487,2488,2502],{},[584,2489,2490,2492,2494,2496,2498,2500],{},[587,2491,666],{},[591,2493,670],{"stretchy":669},[587,2495,589],{},[591,2497,593],{},[587,2499,596],{},[591,2501,675],{"stretchy":669},[598,2503,2504],{"encoding":600},"P(A \\cup B)",[568,2506,2508,2532],{"className":2507,"ariaHidden":606},[605],[568,2509,2511,2514,2517,2520,2523,2526,2529],{"className":2510},[610],[568,2512],{"className":2513,"style":699},[614],[568,2515,666],{"className":2516,"style":703},[619,620],[568,2518,670],{"className":2519},[707],[568,2521,589],{"className":2522},[619,620],[568,2524],{"className":2525,"style":625},[624],[568,2527,593],{"className":2528},[629],[568,2530],{"className":2531,"style":625},[624],[568,2533,2535,2538,2541],{"className":2534},[610],[568,2536],{"className":2537,"style":699},[614],[568,2539,596],{"className":2540,"style":642},[619,620],[568,2542,675],{"className":2543},[714]," enthält den Fall, dass beide eintreten. Für „genau eines von beiden“ zieht man ",[568,2546,2548,2571],{"className":2547},[571],[568,2549,2551],{"className":2550},[575],[577,2552,2553],{"xmlns":579},[581,2554,2555,2569],{},[584,2556,2557,2559,2561,2563,2565,2567],{},[587,2558,666],{},[591,2560,670],{"stretchy":669},[587,2562,589],{},[591,2564,767],{},[587,2566,596],{},[591,2568,675],{"stretchy":669},[598,2570,774],{"encoding":600},[568,2572,2574,2598],{"className":2573,"ariaHidden":606},[605],[568,2575,2577,2580,2583,2586,2589,2592,2595],{"className":2576},[610],[568,2578],{"className":2579,"style":699},[614],[568,2581,666],{"className":2582,"style":703},[619,620],[568,2584,670],{"className":2585},[707],[568,2587,589],{"className":2588},[619,620],[568,2590],{"className":2591,"style":625},[624],[568,2593,767],{"className":2594},[629],[568,2596],{"className":2597,"style":625},[624],[568,2599,2601,2604,2607],{"className":2600},[610],[568,2602],{"className":2603,"style":699},[614],[568,2605,596],{"className":2606,"style":642},[619,620],[568,2608,675],{"className":2609},[714]," zweimal ab.",[2275,2612,2613,2678,2679,2761,2762,846,2790,2818,2819,3108,3109,1115],{},[568,2614,2616,2639],{"className":2615},[571],[568,2617,2619],{"className":2618},[575],[577,2620,2621],{"xmlns":579},[581,2622,2623,2637],{},[584,2624,2625,2627,2629,2631,2633,2635],{},[587,2626,666],{},[591,2628,670],{"stretchy":669},[587,2630,589],{},[591,2632,767],{},[587,2634,596],{},[591,2636,675],{"stretchy":669},[598,2638,774],{"encoding":600},[568,2640,2642,2666],{"className":2641,"ariaHidden":606},[605],[568,2643,2645,2648,2651,2654,2657,2660,2663],{"className":2644},[610],[568,2646],{"className":2647,"style":699},[614],[568,2649,666],{"className":2650,"style":703},[619,620],[568,2652,670],{"className":2653},[707],[568,2655,589],{"className":2656},[619,620],[568,2658],{"className":2659,"style":625},[624],[568,2661,767],{"className":2662},[629],[568,2664],{"className":2665,"style":625},[624],[568,2667,2669,2672,2675],{"className":2668},[610],[568,2670],{"className":2671,"style":699},[614],[568,2673,596],{"className":2674,"style":642},[619,620],[568,2676,675],{"className":2677},[714]," einfach als ",[568,2680,2682,2713],{"className":2681},[571],[568,2683,2685],{"className":2684},[575],[577,2686,2687],{"xmlns":579},[581,2688,2689,2710],{},[584,2690,2691,2693,2695,2697,2699,2702,2704,2706,2708],{},[587,2692,666],{},[591,2694,670],{"stretchy":669},[587,2696,589],{},[591,2698,675],{"stretchy":669},[591,2700,2701],{},"⋅",[587,2703,666],{},[591,2705,670],{"stretchy":669},[587,2707,596],{},[591,2709,675],{"stretchy":669},[598,2711,2712],{"encoding":600},"P(A) \\cdot P(B)",[568,2714,2716,2743],{"className":2715,"ariaHidden":606},[605],[568,2717,2719,2722,2725,2728,2731,2734,2737,2740],{"className":2718},[610],[568,2720],{"className":2721,"style":699},[614],[568,2723,666],{"className":2724,"style":703},[619,620],[568,2726,670],{"className":2727},[707],[568,2729,589],{"className":2730},[619,620],[568,2732,675],{"className":2733},[714],[568,2735],{"className":2736,"style":625},[624],[568,2738,2701],{"className":2739},[629],[568,2741],{"className":2742,"style":625},[624],[568,2744,2746,2749,2752,2755,2758],{"className":2745},[610],[568,2747],{"className":2748,"style":699},[614],[568,2750,666],{"className":2751,"style":703},[619,620],[568,2753,670],{"className":2754},[707],[568,2756,596],{"className":2757,"style":642},[619,620],[568,2759,675],{"className":2760},[714]," berechnen. Das stimmt nur, wenn ",[568,2763,2765,2778],{"className":2764},[571],[568,2766,2768],{"className":2767},[575],[577,2769,2770],{"xmlns":579},[581,2771,2772,2776],{},[584,2773,2774],{},[587,2775,589],{},[598,2777,589],{"encoding":600},[568,2779,2781],{"className":2780,"ariaHidden":606},[605],[568,2782,2784,2787],{"className":2783},[610],[568,2785],{"className":2786,"style":615},[614],[568,2788,589],{"className":2789},[619,620],[568,2791,2793,2806],{"className":2792},[571],[568,2794,2796],{"className":2795},[575],[577,2797,2798],{"xmlns":579},[581,2799,2800,2804],{},[584,2801,2802],{},[587,2803,596],{},[598,2805,596],{"encoding":600},[568,2807,2809],{"className":2808,"ariaHidden":606},[605],[568,2810,2812,2815],{"className":2811},[610],[568,2813],{"className":2814,"style":615},[614],[568,2816,596],{"className":2817,"style":642},[619,620]," unabhängig sind. Im Würfelbeispiel wäre ",[568,2820,2822,2856],{"className":2821},[571],[568,2823,2825],{"className":2824},[575],[577,2826,2827],{"xmlns":579},[581,2828,2829,2853],{},[584,2830,2831,2837,2839,2845,2847],{},[1436,2832,2833,2835],{},[908,2834,2460],{},[908,2836,1171],{},[591,2838,2701],{},[1436,2840,2841,2843],{},[908,2842,2460],{},[908,2844,1171],{},[591,2846,906],{},[1436,2848,2849,2851],{},[908,2850,2460],{},[908,2852,1177],{},[598,2854,2855],{"encoding":600},"\\frac{1}{2} \\cdot \\frac{1}{2} = \\frac{1}{4}",[568,2857,2859,2951,3034],{"className":2858,"ariaHidden":606},[605],[568,2860,2862,2866,2942,2945,2948],{"className":2861},[610],[568,2863],{"className":2864,"style":2865},[614],"height:1.1901em;vertical-align:-0.345em;",[568,2867,2869,2872,2939],{"className":2868},[619],[568,2870],{"className":2871},[707,1540],[568,2873,2875],{"className":2874},[1436],[568,2876,2878,2930],{"className":2877},[1547,1548],[568,2879,2881,2927],{"className":2880},[1552],[568,2882,2885,2904,2912],{"className":2883,"style":2884},[1556],"height:0.8451em;",[568,2886,2888,2891],{"style":2887},"top:-2.655em;",[568,2889],{"className":2890,"style":1565},[1564],[568,2892,2898],{"className":2893},[2894,2895,2896,2897],"sizing","reset-size6","size3","mtight",[568,2899,2901],{"className":2900},[619,2897],[568,2902,1171],{"className":2903},[619,2897],[568,2905,2906,2909],{"style":1574},[568,2907],{"className":2908,"style":1565},[1564],[568,2910],{"className":2911,"style":1582},[1581],[568,2913,2915,2918],{"style":2914},"top:-3.394em;",[568,2916],{"className":2917,"style":1565},[1564],[568,2919,2921],{"className":2920},[2894,2895,2896,2897],[568,2922,2924],{"className":2923},[619,2897],[568,2925,2460],{"className":2926},[619,2897],[568,2928,1599],{"className":2929},[1598],[568,2931,2933],{"className":2932},[1552],[568,2934,2937],{"className":2935,"style":2936},[1556],"height:0.345em;",[568,2938],{},[568,2940],{"className":2941},[714,1540],[568,2943],{"className":2944,"style":625},[624],[568,2946,2701],{"className":2947},[629],[568,2949],{"className":2950,"style":625},[624],[568,2952,2954,2957,3025,3028,3031],{"className":2953},[610],[568,2955],{"className":2956,"style":2865},[614],[568,2958,2960,2963,3022],{"className":2959},[619],[568,2961],{"className":2962},[707,1540],[568,2964,2966],{"className":2965},[1436],[568,2967,2969,3014],{"className":2968},[1547,1548],[568,2970,2972,3011],{"className":2971},[1552],[568,2973,2975,2989,2997],{"className":2974,"style":2884},[1556],[568,2976,2977,2980],{"style":2887},[568,2978],{"className":2979,"style":1565},[1564],[568,2981,2983],{"className":2982},[2894,2895,2896,2897],[568,2984,2986],{"className":2985},[619,2897],[568,2987,1171],{"className":2988},[619,2897],[568,2990,2991,2994],{"style":1574},[568,2992],{"className":2993,"style":1565},[1564],[568,2995],{"className":2996,"style":1582},[1581],[568,2998,2999,3002],{"style":2914},[568,3000],{"className":3001,"style":1565},[1564],[568,3003,3005],{"className":3004},[2894,2895,2896,2897],[568,3006,3008],{"className":3007},[619,2897],[568,3009,2460],{"className":3010},[619,2897],[568,3012,1599],{"className":3013},[1598],[568,3015,3017],{"className":3016},[1552],[568,3018,3020],{"className":3019,"style":2936},[1556],[568,3021],{},[568,3023],{"className":3024},[714,1540],[568,3026],{"className":3027,"style":956},[624],[568,3029,906],{"className":3030},[960],[568,3032],{"className":3033,"style":956},[624],[568,3035,3037,3040],{"className":3036},[610],[568,3038],{"className":3039,"style":2865},[614],[568,3041,3043,3046,3105],{"className":3042},[619],[568,3044],{"className":3045},[707,1540],[568,3047,3049],{"className":3048},[1436],[568,3050,3052,3097],{"className":3051},[1547,1548],[568,3053,3055,3094],{"className":3054},[1552],[568,3056,3058,3072,3080],{"className":3057,"style":2884},[1556],[568,3059,3060,3063],{"style":2887},[568,3061],{"className":3062,"style":1565},[1564],[568,3064,3066],{"className":3065},[2894,2895,2896,2897],[568,3067,3069],{"className":3068},[619,2897],[568,3070,1177],{"className":3071},[619,2897],[568,3073,3074,3077],{"style":1574},[568,3075],{"className":3076,"style":1565},[1564],[568,3078],{"className":3079,"style":1582},[1581],[568,3081,3082,3085],{"style":2914},[568,3083],{"className":3084,"style":1565},[1564],[568,3086,3088],{"className":3087},[2894,2895,2896,2897],[568,3089,3091],{"className":3090},[619,2897],[568,3092,2460],{"className":3093},[619,2897],[568,3095,1599],{"className":3096},[1598],[568,3098,3100],{"className":3099},[1552],[568,3101,3103],{"className":3102,"style":2936},[1556],[568,3104],{},[568,3106],{"className":3107},[714,1540]," falsch, richtig ist ",[568,3110,3112,3138],{"className":3111},[571],[568,3113,3115],{"className":3114},[575],[577,3116,3117],{"xmlns":579},[581,3118,3119,3135],{},[584,3120,3121,3127,3129],{},[1436,3122,3123,3125],{},[908,3124,1171],{},[908,3126,1182],{},[591,3128,906],{},[1436,3130,3131,3133],{},[908,3132,2460],{},[908,3134,1440],{},[598,3136,3137],{"encoding":600},"\\frac{2}{6} = \\frac{1}{3}",[568,3139,3141,3224],{"className":3140,"ariaHidden":606},[605],[568,3142,3144,3147,3215,3218,3221],{"className":3143},[610],[568,3145],{"className":3146,"style":2865},[614],[568,3148,3150,3153,3212],{"className":3149},[619],[568,3151],{"className":3152},[707,1540],[568,3154,3156],{"className":3155},[1436],[568,3157,3159,3204],{"className":3158},[1547,1548],[568,3160,3162,3201],{"className":3161},[1552],[568,3163,3165,3179,3187],{"className":3164,"style":2884},[1556],[568,3166,3167,3170],{"style":2887},[568,3168],{"className":3169,"style":1565},[1564],[568,3171,3173],{"className":3172},[2894,2895,2896,2897],[568,3174,3176],{"className":3175},[619,2897],[568,3177,1182],{"className":3178},[619,2897],[568,3180,3181,3184],{"style":1574},[568,3182],{"className":3183,"style":1565},[1564],[568,3185],{"className":3186,"style":1582},[1581],[568,3188,3189,3192],{"style":2914},[568,3190],{"className":3191,"style":1565},[1564],[568,3193,3195],{"className":3194},[2894,2895,2896,2897],[568,3196,3198],{"className":3197},[619,2897],[568,3199,1171],{"className":3200},[619,2897],[568,3202,1599],{"className":3203},[1598],[568,3205,3207],{"className":3206},[1552],[568,3208,3210],{"className":3209,"style":2936},[1556],[568,3211],{},[568,3213],{"className":3214},[714,1540],[568,3216],{"className":3217,"style":956},[624],[568,3219,906],{"className":3220},[960],[568,3222],{"className":3223,"style":956},[624],[568,3225,3227,3230],{"className":3226},[610],[568,3228],{"className":3229,"style":2865},[614],[568,3231,3233,3236,3295],{"className":3232},[619],[568,3234],{"className":3235},[707,1540],[568,3237,3239],{"className":3238},[1436],[568,3240,3242,3287],{"className":3241},[1547,1548],[568,3243,3245,3284],{"className":3244},[1552],[568,3246,3248,3262,3270],{"className":3247,"style":2884},[1556],[568,3249,3250,3253],{"style":2887},[568,3251],{"className":3252,"style":1565},[1564],[568,3254,3256],{"className":3255},[2894,2895,2896,2897],[568,3257,3259],{"className":3258},[619,2897],[568,3260,1440],{"className":3261},[619,2897],[568,3263,3264,3267],{"style":1574},[568,3265],{"className":3266,"style":1565},[1564],[568,3268],{"className":3269,"style":1582},[1581],[568,3271,3272,3275],{"style":2914},[568,3273],{"className":3274,"style":1565},[1564],[568,3276,3278],{"className":3277},[2894,2895,2896,2897],[568,3279,3281],{"className":3280},[619,2897],[568,3282,2460],{"className":3283},[619,2897],[568,3285,1599],{"className":3286},[1598],[568,3288,3290],{"className":3289},[1552],[568,3291,3293],{"className":3292,"style":2936},[1556],[568,3294],{},[568,3296],{"className":3297},[714,1540],[2275,3299,3300,3301,1115],{},"Bei unvereinbaren Ereignissen trotzdem etwas abziehen: Für „1“ oder „2“ beim Würfel gilt einfach ",[568,3302,3304,3338],{"className":3303},[571],[568,3305,3307],{"className":3306},[575],[577,3308,3309],{"xmlns":579},[581,3310,3311,3335],{},[584,3312,3313,3319,3321,3327,3329],{},[1436,3314,3315,3317],{},[908,3316,2460],{},[908,3318,1182],{},[591,3320,678],{},[1436,3322,3323,3325],{},[908,3324,2460],{},[908,3326,1182],{},[591,3328,906],{},[1436,3330,3331,3333],{},[908,3332,2460],{},[908,3334,1440],{},[598,3336,3337],{"encoding":600},"\\frac{1}{6} + \\frac{1}{6} = \\frac{1}{3}",[568,3339,3341,3424,3507],{"className":3340,"ariaHidden":606},[605],[568,3342,3344,3347,3415,3418,3421],{"className":3343},[610],[568,3345],{"className":3346,"style":2865},[614],[568,3348,3350,3353,3412],{"className":3349},[619],[568,3351],{"className":3352},[707,1540],[568,3354,3356],{"className":3355},[1436],[568,3357,3359,3404],{"className":3358},[1547,1548],[568,3360,3362,3401],{"className":3361},[1552],[568,3363,3365,3379,3387],{"className":3364,"style":2884},[1556],[568,3366,3367,3370],{"style":2887},[568,3368],{"className":3369,"style":1565},[1564],[568,3371,3373],{"className":3372},[2894,2895,2896,2897],[568,3374,3376],{"className":3375},[619,2897],[568,3377,1182],{"className":3378},[619,2897],[568,3380,3381,3384],{"style":1574},[568,3382],{"className":3383,"style":1565},[1564],[568,3385],{"className":3386,"style":1582},[1581],[568,3388,3389,3392],{"style":2914},[568,3390],{"className":3391,"style":1565},[1564],[568,3393,3395],{"className":3394},[2894,2895,2896,2897],[568,3396,3398],{"className":3397},[619,2897],[568,3399,2460],{"className":3400},[619,2897],[568,3402,1599],{"className":3403},[1598],[568,3405,3407],{"className":3406},[1552],[568,3408,3410],{"className":3409,"style":2936},[1556],[568,3411],{},[568,3413],{"className":3414},[714,1540],[568,3416],{"className":3417,"style":625},[624],[568,3419,678],{"className":3420},[629],[568,3422],{"className":3423,"style":625},[624],[568,3425,3427,3430,3498,3501,3504],{"className":3426},[610],[568,3428],{"className":3429,"style":2865},[614],[568,3431,3433,3436,3495],{"className":3432},[619],[568,3434],{"className":3435},[707,1540],[568,3437,3439],{"className":3438},[1436],[568,3440,3442,3487],{"className":3441},[1547,1548],[568,3443,3445,3484],{"className":3444},[1552],[568,3446,3448,3462,3470],{"className":3447,"style":2884},[1556],[568,3449,3450,3453],{"style":2887},[568,3451],{"className":3452,"style":1565},[1564],[568,3454,3456],{"className":3455},[2894,2895,2896,2897],[568,3457,3459],{"className":3458},[619,2897],[568,3460,1182],{"className":3461},[619,2897],[568,3463,3464,3467],{"style":1574},[568,3465],{"className":3466,"style":1565},[1564],[568,3468],{"className":3469,"style":1582},[1581],[568,3471,3472,3475],{"style":2914},[568,3473],{"className":3474,"style":1565},[1564],[568,3476,3478],{"className":3477},[2894,2895,2896,2897],[568,3479,3481],{"className":3480},[619,2897],[568,3482,2460],{"className":3483},[619,2897],[568,3485,1599],{"className":3486},[1598],[568,3488,3490],{"className":3489},[1552],[568,3491,3493],{"className":3492,"style":2936},[1556],[568,3494],{},[568,3496],{"className":3497},[714,1540],[568,3499],{"className":3500,"style":956},[624],[568,3502,906],{"className":3503},[960],[568,3505],{"className":3506,"style":956},[624],[568,3508,3510,3513],{"className":3509},[610],[568,3511],{"className":3512,"style":2865},[614],[568,3514,3516,3519,3578],{"className":3515},[619],[568,3517],{"className":3518},[707,1540],[568,3520,3522],{"className":3521},[1436],[568,3523,3525,3570],{"className":3524},[1547,1548],[568,3526,3528,3567],{"className":3527},[1552],[568,3529,3531,3545,3553],{"className":3530,"style":2884},[1556],[568,3532,3533,3536],{"style":2887},[568,3534],{"className":3535,"style":1565},[1564],[568,3537,3539],{"className":3538},[2894,2895,2896,2897],[568,3540,3542],{"className":3541},[619,2897],[568,3543,1440],{"className":3544},[619,2897],[568,3546,3547,3550],{"style":1574},[568,3548],{"className":3549,"style":1565},[1564],[568,3551],{"className":3552,"style":1582},[1581],[568,3554,3555,3558],{"style":2914},[568,3556],{"className":3557,"style":1565},[1564],[568,3559,3561],{"className":3560},[2894,2895,2896,2897],[568,3562,3564],{"className":3563},[619,2897],[568,3565,2460],{"className":3566},[619,2897],[568,3568,1599],{"className":3569},[1598],[568,3571,3573],{"className":3572},[1552],[568,3574,3576],{"className":3575,"style":2936},[1556],[568,3577],{},[568,3579],{"className":3580},[714,1540],{"title":3582,"searchDepth":3583,"depth":3583,"links":3584},"",2,[3585,3586,3587],{"id":561,"depth":3583,"text":562},{"id":1118,"depth":3583,"text":1119},{"id":2269,"depth":3583,"text":2270},[3589,3592,3595,3598,3601,3604,3607,3610],{"lhs":3590,"rhs":3591},"(u + w) + (v + w) - w","u + v + w",{"lhs":3593,"rhs":3594},"3\u002F6 + 3\u002F6 - 2\u002F6","2\u002F3",{"lhs":3596,"rhs":3597},"0.40 + 0.55 - 0.20","0.75",{"lhs":3599,"rhs":3600},"1 - 0.75","0.25",{"lhs":3602,"rhs":3603},"0.40 + 0.55","0.95",{"lhs":3605,"rhs":3606},"1\u002F2 * 1\u002F2","1\u002F4",{"lhs":3608,"rhs":3609},"2\u002F6","1\u002F3",{"lhs":3611,"rhs":3609},"1\u002F6 + 1\u002F6",null,"md","addition-rule","P(A \\cup B) = P(A) + P(B) - P(A \\cap B)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∪\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∩\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(A \\cup B) = P(A) + P(B) - P(A \\cap B)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fadditionssatz",[],[3623,3624,3625,3626],"complement-probability","laplace-probability","path-addition-rule","inclusion-exclusion",{"title":548,"description":3582},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fadditionssatz","Die Wahrscheinlichkeit für A oder B ist P(A) plus P(B) minus die Wahrscheinlichkeit, dass beide eintreten.",[3631,3632,3633,3634],"vereinigung","schnittmenge","oder-ereignis","wahrscheinlichkeit",[3636,3640,3643,3646],{"symbol":3637,"meaning":3638,"symbolHtml":3639},"A, B","zwei Ereignisse desselben Zufallsexperiments","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A, B\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2504,"meaning":3641,"symbolHtml":3642},"Wahrscheinlichkeit, dass A oder B (oder beide) eintreten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∪\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(A \\cup B)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":774,"meaning":3644,"symbolHtml":3645},"Wahrscheinlichkeit, dass A und B gleichzeitig eintreten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∩\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(A \\cap B)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3647,"meaning":3648,"symbolHtml":3649},"P(A), P(B)","Wahrscheinlichkeiten der einzelnen Ereignisse","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(A), P(B)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan 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