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1175,1176,1179],{"style":936},[590,1177],{"className":1178,"style":927},[926],[590,1180],{"className":1181,"style":944},[943],[590,1183,1184,1187],{"style":947},[590,1185],{"className":1186,"style":927},[926],[590,1188,1190],{"className":1189},[633],[590,1191,656],{"className":1192},[633],[590,1194,961],{"className":1195},[960],[590,1197,1199],{"className":1198},[914],[590,1200,1202],{"className":1201,"style":968},[918],[590,1203],{},[590,1205],{"className":1206},[876,902],[590,1208],{"className":1209,"style":881},[880],[590,1211,840],{"className":1212},[885],[590,1214],{"className":1215,"style":881},[880],[590,1217,1219,1223,1227,1235],{"className":1218},[624],[590,1220],{"className":1221,"style":1222},[628],"height:0.8389em;vertical-align:-0.1944em;",[590,1224,1226],{"className":1225},[633],"0",[590,1228,1230],{"className":1229},[633],[590,1231,1234],{"className":1232},[1233],"mpunct",",",[590,1236,1238],{"className":1237},[633],"107",[564,1240,1241,1242,1245],{},"Dasselbe ",[568,1243,1244],{},"mit Zurücklegen",": Die zweite Stufe sieht genauso aus wie die erste.",[590,1247,1249],{"className":1248},[769],[590,1250,1252,1303],{"className":1251},[593],[590,1253,1255],{"className":1254},[597],[599,1256,1257],{"xmlns":601,"display":778},[603,1258,1259,1300],{},[606,1260,1261,1263,1265,1267,1269,1271,1277,1279,1285,1287,1295,1297],{},[784,1262,786],{},[788,1264,791],{"stretchy":790},[793,1266,795],{},[788,1268,798],{"stretchy":790},[788,1270,801],{},[803,1272,1273,1275],{},[609,1274,656],{},[609,1276,809],{},[788,1278,812],{},[803,1280,1281,1283],{},[609,1282,656],{},[609,1284,809],{},[788,1286,801],{},[803,1288,1289,1292],{},[609,1290,1291],{},"9",[609,1293,1294],{},"64",[788,1296,840],{},[609,1298,1299],{},"0,141",[613,1301,1302],{"encoding":615},"P(\\text{rot, rot}) = \\frac{3}{8} \\cdot \\frac{3}{8} = \\frac{9}{64} \\approx 0{,}141",[590,1304,1306,1336,1413,1490,1567],{"className":1305,"ariaHidden":620},[619],[590,1307,1309,1312,1315,1318,1324,1327,1330,1333],{"className":1308},[624],[590,1310],{"className":1311,"style":856},[628],[590,1313,786],{"className":1314,"style":861},[633,860],[590,1316,791],{"className":1317},[865],[590,1319,1321],{"className":1320},[633,869],[590,1322,795],{"className":1323},[633],[590,1325,798],{"className":1326},[876],[590,1328],{"className":1329,"style":881},[880],[590,1331,801],{"className":1332},[885],[590,1334],{"className":1335,"style":881},[880],[590,1337,1339,1342,1404,1407,1410],{"className":1338},[624],[590,1340],{"className":1341,"style":895},[628],[590,1343,1345,1348,1401],{"className":1344},[633],[590,1346],{"className":1347},[865,902],[590,1349,1351],{"className":1350},[803],[590,1352,1354,1393],{"className":1353},[909,910],[590,1355,1357,1390],{"className":1356},[914],[590,1358,1360,1371,1379],{"className":1359,"style":919},[918],[590,1361,1362,1365],{"style":922},[590,1363],{"className":1364,"style":927},[926],[590,1366,1368],{"className":1367},[633],[590,1369,809],{"className":1370},[633],[590,1372,1373,1376],{"style":936},[590,1374],{"className":1375,"style":927},[926],[590,1377],{"className":1378,"style":944},[943],[590,1380,1381,1384],{"style":947},[590,1382],{"className":1383,"style":927},[926],[590,1385,1387],{"className":1386},[633],[590,1388,656],{"className":1389},[633],[590,1391,961],{"className":1392},[960],[590,1394,1396],{"className":1395},[914],[590,1397,1399],{"className":1398,"style":968},[918],[590,1400],{},[590,1402],{"className":1403},[876,902],[590,1405],{"className":1406,"style":977},[880],[590,1408,812],{"className":1409},[981],[590,1411],{"className":1412,"style":977},[880],[590,1414,1416,1419,1481,1484,1487],{"className":1415},[624],[590,1417],{"className":1418,"style":895},[628],[590,1420,1422,1425,1478],{"className":1421},[633],[590,1423],{"className":1424},[865,902],[590,1426,1428],{"className":1427},[803],[590,1429,1431,1470],{"className":1430},[909,910],[590,1432,1434,1467],{"className":1433},[914],[590,1435,1437,1448,1456],{"className":1436,"style":919},[918],[590,1438,1439,1442],{"style":922},[590,1440],{"className":1441,"style":927},[926],[590,1443,1445],{"className":1444},[633],[590,1446,809],{"className":1447},[633],[590,1449,1450,1453],{"style":936},[590,1451],{"className":1452,"style":927},[926],[590,1454],{"className":1455,"style":944},[943],[590,1457,1458,1461],{"style":947},[590,1459],{"className":1460,"style":927},[926],[590,1462,1464],{"className":1463},[633],[590,1465,656],{"className":1466},[633],[590,1468,961],{"className":1469},[960],[590,1471,1473],{"className":1472},[914],[590,1474,1476],{"className":1475,"style":968},[918],[590,1477],{},[590,1479],{"className":1480},[876,902],[590,1482],{"className":1483,"style":881},[880],[590,1485,801],{"className":1486},[885],[590,1488],{"className":1489,"style":881},[880],[590,1491,1493,1496,1558,1561,1564],{"className":1492},[624],[590,1494],{"className":1495,"style":895},[628],[590,1497,1499,1502,1555],{"className":1498},[633],[590,1500],{"className":1501},[865,902],[590,1503,1505],{"className":1504},[803],[590,1506,1508,1547],{"className":1507},[909,910],[590,1509,1511,1544],{"className":1510},[914],[590,1512,1514,1525,1533],{"className":1513,"style":919},[918],[590,1515,1516,1519],{"style":922},[590,1517],{"className":1518,"style":927},[926],[590,1520,1522],{"className":1521},[633],[590,1523,1294],{"className":1524},[633],[590,1526,1527,1530],{"style":936},[590,1528],{"className":1529,"style":927},[926],[590,1531],{"className":1532,"style":944},[943],[590,1534,1535,1538],{"style":947},[590,1536],{"className":1537,"style":927},[926],[590,1539,1541],{"className":1540},[633],[590,1542,1291],{"className":1543},[633],[590,1545,961],{"className":1546},[960],[590,1548,1550],{"className":1549},[914],[590,1551,1553],{"className":1552,"style":968},[918],[590,1554],{},[590,1556],{"className":1557},[876,902],[590,1559],{"className":1560,"style":881},[880],[590,1562,840],{"className":1563},[885],[590,1565],{"className":1566,"style":881},[880],[590,1568,1570,1573,1576,1582],{"className":1569},[624],[590,1571],{"className":1572,"style":1222},[628],[590,1574,1226],{"className":1575},[633],[590,1577,1579],{"className":1578},[633],[590,1580,1234],{"className":1581},[1233],[590,1583,1585],{"className":1584},[633],"141",[564,1587,1588],{},"Kontrolle ohne Zurücklegen: Alle vier Pfade zusammen ergeben",[590,1590,1592],{"className":1591},[769],[590,1593,1595,1699],{"className":1594},[593],[590,1596,1598],{"className":1597},[597],[599,1599,1600],{"xmlns":601,"display":778},[603,1601,1602,1696],{},[606,1603,1604,1610,1612,1618,1621,1627,1629,1635,1637,1643,1645,1651,1653,1659,1661,1668,1670,1692,1694],{},[803,1605,1606,1608],{},[609,1607,656],{},[609,1609,809],{},[788,1611,812],{},[803,1613,1614,1616],{},[609,1615,720],{},[609,1617,750],{},[788,1619,1620],{},"+",[803,1622,1623,1625],{},[609,1624,656],{},[609,1626,809],{},[788,1628,812],{},[803,1630,1631,1633],{},[609,1632,686],{},[609,1634,750],{},[788,1636,1620],{},[803,1638,1639,1641],{},[609,1640,686],{},[609,1642,809],{},[788,1644,812],{},[803,1646,1647,1649],{},[609,1648,656],{},[609,1650,750],{},[788,1652,1620],{},[803,1654,1655,1657],{},[609,1656,686],{},[609,1658,809],{},[788,1660,812],{},[803,1662,1663,1666],{},[609,1664,1665],{},"4",[609,1667,750],{},[788,1669,801],{},[803,1671,1672,1690],{},[606,1673,1674,1676,1678,1681,1683,1685,1687],{},[609,1675,825],{},[788,1677,1620],{},[609,1679,1680],{},"15",[788,1682,1620],{},[609,1684,1680],{},[788,1686,1620],{},[609,1688,1689],{},"20",[609,1691,828],{},[788,1693,801],{},[609,1695,611],{},[613,1697,1698],{"encoding":615},"\\frac{3}{8} \\cdot \\frac{2}{7} + \\frac{3}{8} \\cdot \\frac{5}{7} + \\frac{5}{8} \\cdot \\frac{3}{7} + \\frac{5}{8} \\cdot \\frac{4}{7} = \\frac{6 + 15 + 15 + 20}{56} = 1",[590,1700,1702,1779,1856,1933,2010,2087,2164,2241,2318,2431],{"className":1701,"ariaHidden":620},[619],[590,1703,1705,1708,1770,1773,1776],{"className":1704},[624],[590,1706],{"className":1707,"style":895},[628],[590,1709,1711,1714,1767],{"className":1710},[633],[590,1712],{"className":1713},[865,902],[590,1715,1717],{"className":1716},[803],[590,1718,1720,1759],{"className":1719},[909,910],[590,1721,1723,1756],{"className":1722},[914],[590,1724,1726,1737,1745],{"className":1725,"style":919},[918],[590,1727,1728,1731],{"style":922},[590,1729],{"className":1730,"style":927},[926],[590,1732,1734],{"className":1733},[633],[590,1735,809],{"className":1736},[633],[590,1738,1739,1742],{"style":936},[590,1740],{"className":1741,"style":927},[926],[590,1743],{"className":1744,"style":944},[943],[590,1746,1747,1750],{"style":947},[590,1748],{"className":1749,"style":927},[926],[590,1751,1753],{"className":1752},[633],[590,1754,656],{"className":1755},[633],[590,1757,961],{"className":1758},[960],[590,1760,1762],{"className":1761},[914],[590,1763,1765],{"className":1764,"style":968},[918],[590,1766],{},[590,1768],{"className":1769},[876,902],[590,1771],{"className":1772,"style":977},[880],[590,1774,812],{"className":1775},[981],[590,1777],{"className":1778,"style":977},[880],[590,1780,1782,1785,1847,1850,1853],{"className":1781},[624],[590,1783],{"className":1784,"style":895},[628],[590,1786,1788,1791,1844],{"className":1787},[633],[590,1789],{"className":1790},[865,902],[590,1792,1794],{"className":1793},[803],[590,1795,1797,1836],{"className":1796},[909,910],[590,1798,1800,1833],{"className":1799},[914],[590,1801,1803,1814,1822],{"className":1802,"style":919},[918],[590,1804,1805,1808],{"style":922},[590,1806],{"className":1807,"style":927},[926],[590,1809,1811],{"className":1810},[633],[590,1812,750],{"className":1813},[633],[590,1815,1816,1819],{"style":936},[590,1817],{"className":1818,"style":927},[926],[590,1820],{"className":1821,"style":944},[943],[590,1823,1824,1827],{"style":947},[590,1825],{"className":1826,"style":927},[926],[590,1828,1830],{"className":1829},[633],[590,1831,720],{"className":1832},[633],[590,1834,961],{"className":1835},[960],[590,1837,1839],{"className":1838},[914],[590,1840,1842],{"className":1841,"style":968},[918],[590,1843],{},[590,1845],{"className":1846},[876,902],[590,1848],{"className":1849,"style":977},[880],[590,1851,1620],{"className":1852},[981],[590,1854],{"className":1855,"style":977},[880],[590,1857,1859,1862,1924,1927,1930],{"className":1858},[624],[590,1860],{"className":1861,"style":895},[628],[590,1863,1865,1868,1921],{"className":1864},[633],[590,1866],{"className":1867},[865,902],[590,1869,1871],{"className":1870},[803],[590,1872,1874,1913],{"className":1873},[909,910],[590,1875,1877,1910],{"className":1876},[914],[590,1878,1880,1891,1899],{"className":1879,"style":919},[918],[590,1881,1882,1885],{"style":922},[590,1883],{"className":1884,"style":927},[926],[590,1886,1888],{"className":1887},[633],[590,1889,809],{"className":1890},[633],[590,1892,1893,1896],{"style":936},[590,1894],{"className":1895,"style":927},[926],[590,1897],{"className":1898,"style":944},[943],[590,1900,1901,1904],{"style":947},[590,1902],{"className":1903,"style":927},[926],[590,1905,1907],{"className":1906},[633],[590,1908,656],{"className":1909},[633],[590,1911,961],{"className":1912},[960],[590,1914,1916],{"className":1915},[914],[590,1917,1919],{"className":1918,"style":968},[918],[590,1920],{},[590,1922],{"className":1923},[876,902],[590,1925],{"className":1926,"style":977},[880],[590,1928,812],{"className":1929},[981],[590,1931],{"className":1932,"style":977},[880],[590,1934,1936,1939,2001,2004,2007],{"className":1935},[624],[590,1937],{"className":1938,"style":895},[628],[590,1940,1942,1945,1998],{"className":1941},[633],[590,1943],{"className":1944},[865,902],[590,1946,1948],{"className":1947},[803],[590,1949,1951,1990],{"className":1950},[909,910],[590,1952,1954,1987],{"className":1953},[914],[590,1955,1957,1968,1976],{"className":1956,"style":919},[918],[590,1958,1959,1962],{"style":922},[590,1960],{"className":1961,"style":927},[926],[590,1963,1965],{"className":1964},[633],[590,1966,750],{"className":1967},[633],[590,1969,1970,1973],{"style":936},[590,1971],{"className":1972,"style":927},[926],[590,1974],{"className":1975,"style":944},[943],[590,1977,1978,1981],{"style":947},[590,1979],{"className":1980,"style":927},[926],[590,1982,1984],{"className":1983},[633],[590,1985,686],{"className":1986},[633],[590,1988,961],{"className":1989},[960],[590,1991,1993],{"className":1992},[914],[590,1994,1996],{"className":1995,"style":968},[918],[590,1997],{},[590,1999],{"className":2000},[876,902],[590,2002],{"className":2003,"style":977},[880],[590,2005,1620],{"className":2006},[981],[590,2008],{"className":2009,"style":977},[880],[590,2011,2013,2016,2078,2081,2084],{"className":2012},[624],[590,2014],{"className":2015,"style":895},[628],[590,2017,2019,2022,2075],{"className":2018},[633],[590,2020],{"className":2021},[865,902],[590,2023,2025],{"className":2024},[803],[590,2026,2028,2067],{"className":2027},[909,910],[590,2029,2031,2064],{"className":2030},[914],[590,2032,2034,2045,2053],{"className":2033,"style":919},[918],[590,2035,2036,2039],{"style":922},[590,2037],{"className":2038,"style":927},[926],[590,2040,2042],{"className":2041},[633],[590,2043,809],{"className":2044},[633],[590,2046,2047,2050],{"style":936},[590,2048],{"className":2049,"style":927},[926],[590,2051],{"className":2052,"style":944},[943],[590,2054,2055,2058],{"style":947},[590,2056],{"className":2057,"style":927},[926],[590,2059,2061],{"className":2060},[633],[590,2062,686],{"className":2063},[633],[590,2065,961],{"className":2066},[960],[590,2068,2070],{"className":2069},[914],[590,2071,2073],{"className":2072,"style":968},[918],[590,2074],{},[590,2076],{"className":2077},[876,902],[590,2079],{"className":2080,"style":977},[880],[590,2082,812],{"className":2083},[981],[590,2085],{"className":2086,"style":977},[880],[590,2088,2090,2093,2155,2158,2161],{"className":2089},[624],[590,2091],{"className":2092,"style":895},[628],[590,2094,2096,2099,2152],{"className":2095},[633],[590,2097],{"className":2098},[865,902],[590,2100,2102],{"className":2101},[803],[590,2103,2105,2144],{"className":2104},[909,910],[590,2106,2108,2141],{"className":2107},[914],[590,2109,2111,2122,2130],{"className":2110,"style":919},[918],[590,2112,2113,2116],{"style":922},[590,2114],{"className":2115,"style":927},[926],[590,2117,2119],{"className":2118},[633],[590,2120,750],{"className":2121},[633],[590,2123,2124,2127],{"style":936},[590,2125],{"className":2126,"style":927},[926],[590,2128],{"className":2129,"style":944},[943],[590,2131,2132,2135],{"style":947},[590,2133],{"className":2134,"style":927},[926],[590,2136,2138],{"className":2137},[633],[590,2139,656],{"className":2140},[633],[590,2142,961],{"className":2143},[960],[590,2145,2147],{"className":2146},[914],[590,2148,2150],{"className":2149,"style":968},[918],[590,2151],{},[590,2153],{"className":2154},[876,902],[590,2156],{"className":2157,"style":977},[880],[590,2159,1620],{"className":2160},[981],[590,2162],{"className":2163,"style":977},[880],[590,2165,2167,2170,2232,2235,2238],{"className":2166},[624],[590,2168],{"className":2169,"style":895},[628],[590,2171,2173,2176,2229],{"className":2172},[633],[590,2174],{"className":2175},[865,902],[590,2177,2179],{"className":2178},[803],[590,2180,2182,2221],{"className":2181},[909,910],[590,2183,2185,2218],{"className":2184},[914],[590,2186,2188,2199,2207],{"className":2187,"style":919},[918],[590,2189,2190,2193],{"style":922},[590,2191],{"className":2192,"style":927},[926],[590,2194,2196],{"className":2195},[633],[590,2197,809],{"className":2198},[633],[590,2200,2201,2204],{"style":936},[590,2202],{"className":2203,"style":927},[926],[590,2205],{"className":2206,"style":944},[943],[590,2208,2209,2212],{"style":947},[590,2210],{"className":2211,"style":927},[926],[590,2213,2215],{"className":2214},[633],[590,2216,686],{"className":2217},[633],[590,2219,961],{"className":2220},[960],[590,2222,2224],{"className":2223},[914],[590,2225,2227],{"className":2226,"style":968},[918],[590,2228],{},[590,2230],{"className":2231},[876,902],[590,2233],{"className":2234,"style":977},[880],[590,2236,812],{"className":2237},[981],[590,2239],{"className":2240,"style":977},[880],[590,2242,2244,2247,2309,2312,2315],{"className":2243},[624],[590,2245],{"className":2246,"style":895},[628],[590,2248,2250,2253,2306],{"className":2249},[633],[590,2251],{"className":2252},[865,902],[590,2254,2256],{"className":2255},[803],[590,2257,2259,2298],{"className":2258},[909,910],[590,2260,2262,2295],{"className":2261},[914],[590,2263,2265,2276,2284],{"className":2264,"style":919},[918],[590,2266,2267,2270],{"style":922},[590,2268],{"className":2269,"style":927},[926],[590,2271,2273],{"className":2272},[633],[590,2274,750],{"className":2275},[633],[590,2277,2278,2281],{"style":936},[590,2279],{"className":2280,"style":927},[926],[590,2282],{"className":2283,"style":944},[943],[590,2285,2286,2289],{"style":947},[590,2287],{"className":2288,"style":927},[926],[590,2290,2292],{"className":2291},[633],[590,2293,1665],{"className":2294},[633],[590,2296,961],{"className":2297},[960],[590,2299,2301],{"className":2300},[914],[590,2302,2304],{"className":2303,"style":968},[918],[590,2305],{},[590,2307],{"className":2308},[876,902],[590,2310],{"className":2311,"style":881},[880],[590,2313,801],{"className":2314},[885],[590,2316],{"className":2317,"style":881},[880],[590,2319,2321,2324,2422,2425,2428],{"className":2320},[624],[590,2322],{"className":2323,"style":895},[628],[590,2325,2327,2330,2419],{"className":2326},[633],[590,2328],{"className":2329},[865,902],[590,2331,2333],{"className":2332},[803],[590,2334,2336,2411],{"className":2335},[909,910],[590,2337,2339,2408],{"className":2338},[914],[590,2340,2342,2353,2361],{"className":2341,"style":919},[918],[590,2343,2344,2347],{"style":922},[590,2345],{"className":2346,"style":927},[926],[590,2348,2350],{"className":2349},[633],[590,2351,828],{"className":2352},[633],[590,2354,2355,2358],{"style":936},[590,2356],{"className":2357,"style":927},[926],[590,2359],{"className":2360,"style":944},[943],[590,2362,2363,2366],{"style":947},[590,2364],{"className":2365,"style":927},[926],[590,2367,2369,2372,2375,2378,2381,2384,2387,2390,2393,2396,2399,2402,2405],{"className":2368},[633],[590,2370,825],{"className":2371},[633],[590,2373],{"className":2374,"style":977},[880],[590,2376,1620],{"className":2377},[981],[590,2379],{"className":2380,"style":977},[880],[590,2382,1680],{"className":2383},[633],[590,2385],{"className":2386,"style":977},[880],[590,2388,1620],{"className":2389},[981],[590,2391],{"className":2392,"style":977},[880],[590,2394,1680],{"className":2395},[633],[590,2397],{"className":2398,"style":977},[880],[590,2400,1620],{"className":2401},[981],[590,2403],{"className":2404,"style":977},[880],[590,2406,1689],{"className":2407},[633],[590,2409,961],{"className":2410},[960],[590,2412,2414],{"className":2413},[914],[590,2415,2417],{"className":2416,"style":968},[918],[590,2418],{},[590,2420],{"className":2421},[876,902],[590,2423],{"className":2424,"style":881},[880],[590,2426,801],{"className":2427},[885],[590,2429],{"className":2430,"style":881},[880],[590,2432,2434,2437],{"className":2433},[624],[590,2435],{"className":2436,"style":629},[628],[590,2438,611],{"className":2439},[633],[559,2441,2443],{"id":2442},"typische-fehler","Typische Fehler",[2445,2446,2447,2679,2682],"ul",{},[2448,2449,2450,2451,2649,2650,2678],"li",{},"Beim Ziehen ohne Zurücklegen die zweite Stufe nicht anpassen und ",[590,2452,2454,2480],{"className":2453},[593],[590,2455,2457],{"className":2456},[597],[599,2458,2459],{"xmlns":601},[603,2460,2461,2477],{},[606,2462,2463,2469,2471],{},[803,2464,2465,2467],{},[609,2466,656],{},[609,2468,809],{},[788,2470,812],{},[803,2472,2473,2475],{},[609,2474,656],{},[609,2476,809],{},[613,2478,2479],{"encoding":615},"\\frac{3}{8} \\cdot \\frac{3}{8}",[590,2481,2483,2575],{"className":2482,"ariaHidden":620},[619],[590,2484,2486,2490,2566,2569,2572],{"className":2485},[624],[590,2487],{"className":2488,"style":2489},[628],"height:1.1901em;vertical-align:-0.345em;",[590,2491,2493,2496,2563],{"className":2492},[633],[590,2494],{"className":2495},[865,902],[590,2497,2499],{"className":2498},[803],[590,2500,2502,2554],{"className":2501},[909,910],[590,2503,2505,2551],{"className":2504},[914],[590,2506,2509,2528,2536],{"className":2507,"style":2508},[918],"height:0.8451em;",[590,2510,2512,2515],{"style":2511},"top:-2.655em;",[590,2513],{"className":2514,"style":927},[926],[590,2516,2522],{"className":2517},[2518,2519,2520,2521],"sizing","reset-size6","size3","mtight",[590,2523,2525],{"className":2524},[633,2521],[590,2526,809],{"className":2527},[633,2521],[590,2529,2530,2533],{"style":936},[590,2531],{"className":2532,"style":927},[926],[590,2534],{"className":2535,"style":944},[943],[590,2537,2539,2542],{"style":2538},"top:-3.394em;",[590,2540],{"className":2541,"style":927},[926],[590,2543,2545],{"className":2544},[2518,2519,2520,2521],[590,2546,2548],{"className":2547},[633,2521],[590,2549,656],{"className":2550},[633,2521],[590,2552,961],{"className":2553},[960],[590,2555,2557],{"className":2556},[914],[590,2558,2561],{"className":2559,"style":2560},[918],"height:0.345em;",[590,2562],{},[590,2564],{"className":2565},[876,902],[590,2567],{"className":2568,"style":977},[880],[590,2570,812],{"className":2571},[981],[590,2573],{"className":2574,"style":977},[880],[590,2576,2578,2581],{"className":2577},[624],[590,2579],{"className":2580,"style":2489},[628],[590,2582,2584,2587,2646],{"className":2583},[633],[590,2585],{"className":2586},[865,902],[590,2588,2590],{"className":2589},[803],[590,2591,2593,2638],{"className":2592},[909,910],[590,2594,2596,2635],{"className":2595},[914],[590,2597,2599,2613,2621],{"className":2598,"style":2508},[918],[590,2600,2601,2604],{"style":2511},[590,2602],{"className":2603,"style":927},[926],[590,2605,2607],{"className":2606},[2518,2519,2520,2521],[590,2608,2610],{"className":2609},[633,2521],[590,2611,809],{"className":2612},[633,2521],[590,2614,2615,2618],{"style":936},[590,2616],{"className":2617,"style":927},[926],[590,2619],{"className":2620,"style":944},[943],[590,2622,2623,2626],{"style":2538},[590,2624],{"className":2625,"style":927},[926],[590,2627,2629],{"className":2628},[2518,2519,2520,2521],[590,2630,2632],{"className":2631},[633,2521],[590,2633,656],{"className":2634},[633,2521],[590,2636,961],{"className":2637},[960],[590,2639,2641],{"className":2640},[914],[590,2642,2644],{"className":2643,"style":2560},[918],[590,2645],{},[590,2647],{"className":2648},[876,902]," rechnen. Nach der ersten Kugel sind nur noch ",[590,2651,2653,2666],{"className":2652},[593],[590,2654,2656],{"className":2655},[597],[599,2657,2658],{"xmlns":601},[603,2659,2660,2664],{},[606,2661,2662],{},[609,2663,750],{},[613,2665,750],{"encoding":615},[590,2667,2669],{"className":2668,"ariaHidden":620},[619],[590,2670,2672,2675],{"className":2671},[624],[590,2673],{"className":2674,"style":629},[628],[590,2676,750],{"className":2677},[633]," Kugeln im Beutel.",[2448,2680,2681],{},"Entlang eines Pfades addieren statt multiplizieren. Addiert wird erst, wenn mehrere Pfade zu einem Ereignis gehören (Pfadadditionsregel).",[2448,2683,2684],{},"Die Wahrscheinlichkeiten in der zweiten Stufe falsch zuordnen, z.B. nach „blau“ die Zahlen von „rot“ eintragen. Jeder Ast hängt davon ab, was vorher passiert ist.",{"title":2686,"searchDepth":2687,"depth":2687,"links":2688},"",2,[2689,2690,2691],{"id":561,"depth":2687,"text":562},{"id":637,"depth":2687,"text":638},{"id":2442,"depth":2687,"text":2443},[2693,2695,2698,2701,2704,2707],{"lhs":2694,"rhs":611},"p*q + p*(1 - q) + (1 - p)*r + (1 - p)*(1 - r)",{"lhs":2696,"rhs":2697},"3\u002F8 * 2\u002F7","3\u002F28",{"lhs":2699,"rhs":2700},"round(3\u002F8 * 2\u002F7, 3)","0.107",{"lhs":2702,"rhs":2703},"3\u002F8 * 3\u002F8","9\u002F64",{"lhs":2705,"rhs":2706},"round(3\u002F8 * 3\u002F8, 3)","0.141",{"lhs":2708,"rhs":611},"3\u002F8 * 2\u002F7 + 3\u002F8 * 5\u002F7 + 5\u002F8 * 3\u002F7 + 5\u002F8 * 4\u002F7",null,"md","path-multiplication-rule","P(\\text{Pfad}) = p_1 \\cdot p_2 \\cdot \\ldots \\cdot p_n","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(\\text{Pfad}) = p_1 \\cdot p_2 \\cdot \\ldots \\cdot p_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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:0.6389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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 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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 mtight\">2\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel",[],[2720,2721,2722,2723],"path-addition-rule","conditional-probability","complement-probability","laplace-probability",{"title":548,"description":2686},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel","Die Wahrscheinlichkeit eines Pfades im Baumdiagramm ist das Produkt der Wahrscheinlichkeiten entlang des Pfades.",[2728,2729,2730,2731],"baumdiagramm","pfadregel","mehrstufiges zufallsexperiment","wahrscheinlichkeit",[2733,2737,2741],{"symbol":2734,"meaning":2735,"symbolHtml":2736},"P(\\text{Pfad})","Wahrscheinlichkeit des Ergebnisses am Ende des Pfades","\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>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(\\text{Pfad})\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 text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2738,"meaning":2739,"symbolHtml":2740},"p_1, p_2, \\ldots, p_n","Wahrscheinlichkeiten an den Ästen entlang des Pfades; ab der zweiten Stufe bedingte Wahrscheinlichkeiten, gegeben den bisherigen Pfad","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1, p_2, \\ldots, p_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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 mtight\">1\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=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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 mtight\">2\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=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2742,"meaning":2743,"symbolHtml":2744},"n","Anzahl der Stufen des Zufallsexperiments","\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 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