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zwei verschiedene Farben gibt es die Pfade rot-blau und blau-rot:",[599,1461,1463],{"className":1462},[739],[599,1464,1466,1528],{"className":1465},[602],[599,1467,1469],{"className":1468},[606],[608,1470,1471],{"xmlns":610,"display":748},[612,1472,1473,1525],{},[615,1474,1475,1477,1479,1482,1484,1486,1492,1494,1500,1502,1508,1510,1516,1518],{},[687,1476,689],{},[691,1478,694],{"stretchy":693},[696,1480,1481],{},"verschiedene Farben",[691,1483,701],{"stretchy":693},[691,1485,764],{},[766,1487,1488,1490],{},[618,1489,620],{},[618,1491,772],{},[691,1493,775],{},[766,1495,1496,1498],{},[618,1497,658],{},[618,1499,783],{},[691,1501,786],{},[766,1503,1504,1506],{},[618,1505,658],{},[618,1507,772],{},[691,1509,775],{},[766,1511,1512,1514],{},[618,1513,620],{},[618,1515,783],{},[691,1517,764],{},[766,1519,1520,1523],{},[618,1521,1522],{},"15",[618,1524,830],{},[622,1526,1527],{"encoding":624},"P(\\text{verschiedene Farben}) = \\frac{3}{8} \\cdot \\frac{5}{7} + \\frac{5}{8} \\cdot \\frac{3}{7} = \\frac{15}{28}",[599,1529,1531,1561,1638,1715,1792,1869],{"className":1530,"ariaHidden":629},[628],[599,1532,1534,1537,1540,1543,1549,1552,1555,1558],{"className":1533},[633],[599,1535],{"className":1536,"style":714},[637],[599,1538,689],{"className":1539,"style":719},[642,718],[599,1541,694],{"className":1542},[723],[599,1544,1546],{"className":1545},[642,727],[599,1547,1481],{"className":1548},[642],[599,1550,701],{"className":1551},[734],[599,1553],{"className":1554,"style":868},[867],[599,1556,764],{"className":1557},[872],[599,1559],{"className":1560,"style":868},[867],[599,1562,1564,1567,1629,1632,1635],{"className":1563},[633],[599,1565],{"className":1566,"style":882},[637],[599,1568,1570,1573,1626],{"className":1569},[642],[599,1571],{"className":1572},[723,889],[599,1574,1576],{"className":1575},[766],[599,1577,1579,1618],{"className":1578},[896,897],[599,1580,1582,1615],{"className":1581},[901],[599,1583,1585,1596,1604],{"className":1584,"style":906},[905],[599,1586,1587,1590],{"style":909},[599,1588],{"className":1589,"style":914},[913],[599,1591,1593],{"className":1592},[642],[599,1594,772],{"className":1595},[642],[599,1597,1598,1601],{"style":923},[599,1599],{"className":1600,"style":914},[913],[599,1602],{"className":1603,"style":931},[930],[599,1605,1606,1609],{"style":934},[599,1607],{"className":1608,"style":914},[913],[599,1610,1612],{"className":1611},[642],[599,1613,620],{"className":1614},[642],[599,1616,948],{"className":1617},[947],[599,1619,1621],{"className":1620},[901],[599,1622,1624],{"className":1623,"style":955},[905],[599,1625],{},[599,1627],{"className":1628},[734,889],[599,1630],{"className":1631,"style":964},[867],[599,1633,775],{"className":1634},[968],[599,1636],{"className":1637,"style":964},[867],[599,1639,1641,1644,1706,1709,1712],{"className":1640},[633],[599,1642],{"className":1643,"style":882},[637],[599,1645,1647,1650,1703],{"className":1646},[642],[599,1648],{"className":1649},[723,889],[599,1651,1653],{"className":1652},[766],[599,1654,1656,1695],{"className":1655},[896,897],[599,1657,1659,1692],{"className":1658},[901],[599,1660,1662,1673,1681],{"className":1661,"style":906},[905],[599,1663,1664,1667],{"style":909},[599,1665],{"className":1666,"style":914},[913],[599,1668,1670],{"className":1669},[642],[599,1671,783],{"className":1672},[642],[599,1674,1675,1678],{"style":923},[599,1676],{"className":1677,"style":914},[913],[599,1679],{"className":1680,"style":931},[930],[599,1682,1683,1686],{"style":934},[599,1684],{"className":1685,"style":914},[913],[599,1687,1689],{"className":1688},[642],[599,1690,658],{"className":1691},[642],[599,1693,948],{"className":1694},[947],[599,1696,1698],{"className":1697},[901],[599,1699,1701],{"className":1700,"style":955},[905],[599,1702],{},[599,1704],{"className":1705},[734,889],[599,1707],{"className":1708,"style":964},[867],[599,1710,786],{"className":1711},[968],[599,1713],{"className":1714,"style":964},[867],[599,1716,1718,1721,1783,1786,1789],{"className":1717},[633],[599,1719],{"className":1720,"style":882},[637],[599,1722,1724,1727,1780],{"className":1723},[642],[599,1725],{"className":1726},[723,889],[599,1728,1730],{"className":1729},[766],[599,1731,1733,1772],{"className":1732},[896,897],[599,1734,1736,1769],{"className":1735},[901],[599,1737,1739,1750,1758],{"className":1738,"style":906},[905],[599,1740,1741,1744],{"style":909},[599,1742],{"className":1743,"style":914},[913],[599,1745,1747],{"className":1746},[642],[599,1748,772],{"className":1749},[642],[599,1751,1752,1755],{"style":923},[599,1753],{"className":1754,"style":914},[913],[599,1756],{"className":1757,"style":931},[930],[599,1759,1760,1763],{"style":934},[599,1761],{"className":1762,"style":914},[913],[599,1764,1766],{"className":1765},[642],[599,1767,658],{"className":1768},[642],[599,1770,948],{"className":1771},[947],[599,1773,1775],{"className":1774},[901],[599,1776,1778],{"className":1777,"style":955},[905],[599,1779],{},[599,1781],{"className":1782},[734,889],[599,1784],{"className":1785,"style":964},[867],[599,1787,775],{"className":1788},[968],[599,1790],{"className":1791,"style":964},[867],[599,1793,1795,1798,1860,1863,1866],{"className":1794},[633],[599,1796],{"className":1797,"style":882},[637],[599,1799,1801,1804,1857],{"className":1800},[642],[599,1802],{"className":1803},[723,889],[599,1805,1807],{"className":1806},[766],[599,1808,1810,1849],{"className":1809},[896,897],[599,1811,1813,1846],{"className":1812},[901],[599,1814,1816,1827,1835],{"className":1815,"style":906},[905],[599,1817,1818,1821],{"style":909},[599,1819],{"className":1820,"style":914},[913],[599,1822,1824],{"className":1823},[642],[599,1825,783],{"className":1826},[642],[599,1828,1829,1832],{"style":923},[599,1830],{"className":1831,"style":914},[913],[599,1833],{"className":1834,"style":931},[930],[599,1836,1837,1840],{"style":934},[599,1838],{"className":1839,"style":914},[913],[599,1841,1843],{"className":1842},[642],[599,1844,620],{"className":1845},[642],[599,1847,948],{"className":1848},[947],[599,1850,1852],{"className":1851},[901],[599,1853,1855],{"className":1854,"style":955},[905],[599,1856],{},[599,1858],{"className":1859},[734,889],[599,1861],{"className":1862,"style":868},[867],[599,1864,764],{"className":1865},[872],[599,1867],{"className":1868,"style":868},[867],[599,1870,1872,1875],{"className":1871},[633],[599,1873],{"className":1874,"style":882},[637],[599,1876,1878,1881,1934],{"className":1877},[642],[599,1879],{"className":1880},[723,889],[599,1882,1884],{"className":1883},[766],[599,1885,1887,1926],{"className":1886},[896,897],[599,1888,1890,1923],{"className":1889},[901],[599,1891,1893,1904,1912],{"className":1892,"style":906},[905],[599,1894,1895,1898],{"style":909},[599,1896],{"className":1897,"style":914},[913],[599,1899,1901],{"className":1900},[642],[599,1902,830],{"className":1903},[642],[599,1905,1906,1909],{"style":923},[599,1907],{"className":1908,"style":914},[913],[599,1910],{"className":1911,"style":931},[930],[599,1913,1914,1917],{"style":934},[599,1915],{"className":1916,"style":914},[913],[599,1918,1920],{"className":1919},[642],[599,1921,1522],{"className":1922},[642],[599,1924,948],{"className":1925},[947],[599,1927,1929],{"className":1928},[901],[599,1930,1932],{"className":1931,"style":955},[905],[599,1933],{},[599,1935],{"className":1936},[734,889],[564,1938,1939,1940,2161],{},"Kontrolle: ",[599,1941,1943,1974],{"className":1942},[602],[599,1944,1946],{"className":1945},[606],[608,1947,1948],{"xmlns":610},[612,1949,1950,1971],{},[615,1951,1952,1958,1960,1966,1968],{},[766,1953,1954,1956],{},[618,1955,827],{},[618,1957,830],{},[691,1959,786],{},[766,1961,1962,1964],{},[618,1963,1522],{},[618,1965,830],{},[691,1967,764],{},[618,1969,1970],{},"1",[622,1972,1973],{"encoding":624},"\\frac{13}{28} + \\frac{15}{28} = 1",[599,1975,1977,2069,2152],{"className":1976,"ariaHidden":629},[628],[599,1978,1980,1984,2060,2063,2066],{"className":1979},[633],[599,1981],{"className":1982,"style":1983},[637],"height:1.1901em;vertical-align:-0.345em;",[599,1985,1987,1990,2057],{"className":1986},[642],[599,1988],{"className":1989},[723,889],[599,1991,1993],{"className":1992},[766],[599,1994,1996,2048],{"className":1995},[896,897],[599,1997,1999,2045],{"className":1998},[901],[599,2000,2003,2022,2030],{"className":2001,"style":2002},[905],"height:0.8451em;",[599,2004,2006,2009],{"style":2005},"top:-2.655em;",[599,2007],{"className":2008,"style":914},[913],[599,2010,2016],{"className":2011},[2012,2013,2014,2015],"sizing","reset-size6","size3","mtight",[599,2017,2019],{"className":2018},[642,2015],[599,2020,830],{"className":2021},[642,2015],[599,2023,2024,2027],{"style":923},[599,2025],{"className":2026,"style":914},[913],[599,2028],{"className":2029,"style":931},[930],[599,2031,2033,2036],{"style":2032},"top:-3.394em;",[599,2034],{"className":2035,"style":914},[913],[599,2037,2039],{"className":2038},[2012,2013,2014,2015],[599,2040,2042],{"className":2041},[642,2015],[599,2043,827],{"className":2044},[642,2015],[599,2046,948],{"className":2047},[947],[599,2049,2051],{"className":2050},[901],[599,2052,2055],{"className":2053,"style":2054},[905],"height:0.345em;",[599,2056],{},[599,2058],{"className":2059},[734,889],[599,2061],{"className":2062,"style":964},[867],[599,2064,786],{"className":2065},[968],[599,2067],{"className":2068,"style":964},[867],[599,2070,2072,2075,2143,2146,2149],{"className":2071},[633],[599,2073],{"className":2074,"style":1983},[637],[599,2076,2078,2081,2140],{"className":2077},[642],[599,2079],{"className":2080},[723,889],[599,2082,2084],{"className":2083},[766],[599,2085,2087,2132],{"className":2086},[896,897],[599,2088,2090,2129],{"className":2089},[901],[599,2091,2093,2107,2115],{"className":2092,"style":2002},[905],[599,2094,2095,2098],{"style":2005},[599,2096],{"className":2097,"style":914},[913],[599,2099,2101],{"className":2100},[2012,2013,2014,2015],[599,2102,2104],{"className":2103},[642,2015],[599,2105,830],{"className":2106},[642,2015],[599,2108,2109,2112],{"style":923},[599,2110],{"className":2111,"style":914},[913],[599,2113],{"className":2114,"style":931},[930],[599,2116,2117,2120],{"style":2032},[599,2118],{"className":2119,"style":914},[913],[599,2121,2123],{"className":2122},[2012,2013,2014,2015],[599,2124,2126],{"className":2125},[642,2015],[599,2127,1522],{"className":2128},[642,2015],[599,2130,948],{"className":2131},[947],[599,2133,2135],{"className":2134},[901],[599,2136,2138],{"className":2137,"style":2054},[905],[599,2139],{},[599,2141],{"className":2142},[734,889],[599,2144],{"className":2145,"style":868},[867],[599,2147,764],{"className":2148},[872],[599,2150],{"className":2151,"style":868},[867],[599,2153,2155,2158],{"className":2154},[633],[599,2156],{"className":2157,"style":638},[637],[599,2159,1970],{"className":2160},[642],".",[564,2163,2164,2165,2204,2205,2244,2245,2284],{},"Beim Basketball trifft Lena den ersten Freiwurf mit ",[599,2166,2168,2183],{"className":2167},[602],[599,2169,2171],{"className":2170},[606],[608,2172,2173],{"xmlns":610},[612,2174,2175,2180],{},[615,2176,2177],{},[618,2178,2179],{},"0,7",[622,2181,2182],{"encoding":624},"0{,}7",[599,2184,2186],{"className":2185,"ariaHidden":629},[628],[599,2187,2189,2192,2195,2201],{"className":2188},[633],[599,2190],{"className":2191,"style":1440},[637],[599,2193,1444],{"className":2194},[642],[599,2196,2198],{"className":2197},[642],[599,2199,1452],{"className":2200},[1451],[599,2202,783],{"className":2203},[642],". Nach einem Treffer trifft sie den zweiten mit ",[599,2206,2208,2223],{"className":2207},[602],[599,2209,2211],{"className":2210},[606],[608,2212,2213],{"xmlns":610},[612,2214,2215,2220],{},[615,2216,2217],{},[618,2218,2219],{},"0,8",[622,2221,2222],{"encoding":624},"0{,}8",[599,2224,2226],{"className":2225,"ariaHidden":629},[628],[599,2227,2229,2232,2235,2241],{"className":2228},[633],[599,2230],{"className":2231,"style":1440},[637],[599,2233,1444],{"className":2234},[642],[599,2236,2238],{"className":2237},[642],[599,2239,1452],{"className":2240},[1451],[599,2242,772],{"className":2243},[642],", nach einem Fehlwurf nur mit ",[599,2246,2248,2263],{"className":2247},[602],[599,2249,2251],{"className":2250},[606],[608,2252,2253],{"xmlns":610},[612,2254,2255,2260],{},[615,2256,2257],{},[618,2258,2259],{},"0,6",[622,2261,2262],{"encoding":624},"0{,}6",[599,2264,2266],{"className":2265,"ariaHidden":629},[628],[599,2267,2269,2272,2275,2281],{"className":2268},[633],[599,2270],{"className":2271,"style":1440},[637],[599,2273,1444],{"className":2274},[642],[599,2276,2278],{"className":2277},[642],[599,2279,1452],{"className":2280},[1451],[599,2282,808],{"className":2283},[642],". Genau ein Treffer gelingt auf zwei Pfaden (Treffer-Fehlwurf und Fehlwurf-Treffer):",[599,2286,2288],{"className":2287},[739],[599,2289,2291,2345],{"className":2290},[602],[599,2292,2294],{"className":2293},[606],[608,2295,2296],{"xmlns":610,"display":748},[612,2297,2298,2342],{},[615,2299,2300,2302,2304,2307,2309,2311,2313,2315,2318,2320,2323,2325,2327,2329,2332,2334,2337,2339],{},[687,2301,689],{},[691,2303,694],{"stretchy":693},[696,2305,2306],{},"genau ein Treffer",[691,2308,701],{"stretchy":693},[691,2310,764],{},[618,2312,2179],{},[691,2314,775],{},[618,2316,2317],{},"0,2",[691,2319,786],{},[618,2321,2322],{},"0,3",[691,2324,775],{},[618,2326,2259],{},[691,2328,764],{},[618,2330,2331],{},"0,14",[691,2333,786],{},[618,2335,2336],{},"0,18",[691,2338,764],{},[618,2340,2341],{},"0,32",[622,2343,2344],{"encoding":624},"P(\\text{genau ein Treffer}) = 0{,}7 \\cdot 0{,}2 + 0{,}3 \\cdot 0{,}6 = 0{,}14 + 0{,}18 = 0{,}32",[599,2346,2348,2378,2405,2432,2459,2486,2514,2542],{"className":2347,"ariaHidden":629},[628],[599,2349,2351,2354,2357,2360,2366,2369,2372,2375],{"className":2350},[633],[599,2352],{"className":2353,"style":714},[637],[599,2355,689],{"className":2356,"style":719},[642,718],[599,2358,694],{"className":2359},[723],[599,2361,2363],{"className":2362},[642,727],[599,2364,2306],{"className":2365},[642],[599,2367,701],{"className":2368},[734],[599,2370],{"className":2371,"style":868},[867],[599,2373,764],{"className":2374},[872],[599,2376],{"className":2377,"style":868},[867],[599,2379,2381,2384,2387,2393,2396,2399,2402],{"className":2380},[633],[599,2382],{"className":2383,"style":1440},[637],[599,2385,1444],{"className":2386},[642],[599,2388,2390],{"className":2389},[642],[599,2391,1452],{"className":2392},[1451],[599,2394,783],{"className":2395},[642],[599,2397],{"className":2398,"style":964},[867],[599,2400,775],{"className":2401},[968],[599,2403],{"className":2404,"style":964},[867],[599,2406,2408,2411,2414,2420,2423,2426,2429],{"className":2407},[633],[599,2409],{"className":2410,"style":1440},[637],[599,2412,1444],{"className":2413},[642],[599,2415,2417],{"className":2416},[642],[599,2418,1452],{"className":2419},[1451],[599,2421,780],{"className":2422},[642],[599,2424],{"className":2425,"style":964},[867],[599,2427,786],{"className":2428},[968],[599,2430],{"className":2431,"style":964},[867],[599,2433,2435,2438,2441,2447,2450,2453,2456],{"className":2434},[633],[599,2436],{"className":2437,"style":1440},[637],[599,2439,1444],{"className":2440},[642],[599,2442,2444],{"className":2443},[642],[599,2445,1452],{"className":2446},[1451],[599,2448,620],{"className":2449},[642],[599,2451],{"className":2452,"style":964},[867],[599,2454,775],{"className":2455},[968],[599,2457],{"className":2458,"style":964},[867],[599,2460,2462,2465,2468,2474,2477,2480,2483],{"className":2461},[633],[599,2463],{"className":2464,"style":1440},[637],[599,2466,1444],{"className":2467},[642],[599,2469,2471],{"className":2470},[642],[599,2472,1452],{"className":2473},[1451],[599,2475,808],{"className":2476},[642],[599,2478],{"className":2479,"style":868},[867],[599,2481,764],{"className":2482},[872],[599,2484],{"className":2485,"style":868},[867],[599,2487,2489,2492,2495,2501,2505,2508,2511],{"className":2488},[633],[599,2490],{"className":2491,"style":1440},[637],[599,2493,1444],{"className":2494},[642],[599,2496,2498],{"className":2497},[642],[599,2499,1452],{"className":2500},[1451],[599,2502,2504],{"className":2503},[642],"14",[599,2506],{"className":2507,"style":964},[867],[599,2509,786],{"className":2510},[968],[599,2512],{"className":2513,"style":964},[867],[599,2515,2517,2520,2523,2529,2533,2536,2539],{"className":2516},[633],[599,2518],{"className":2519,"style":1440},[637],[599,2521,1444],{"className":2522},[642],[599,2524,2526],{"className":2525},[642],[599,2527,1452],{"className":2528},[1451],[599,2530,2532],{"className":2531},[642],"18",[599,2534],{"className":2535,"style":868},[867],[599,2537,764],{"className":2538},[872],[599,2540],{"className":2541,"style":868},[867],[599,2543,2545,2548,2551,2557],{"className":2544},[633],[599,2546],{"className":2547,"style":1440},[637],[599,2549,1444],{"className":2550},[642],[599,2552,2554],{"className":2553},[642],[599,2555,1452],{"className":2556},[1451],[599,2558,2560],{"className":2559},[642],"32",[559,2562,2564],{"id":2563},"typische-fehler","Typische Fehler",[2566,2567,2568,2575,2578],"ul",{},[582,2569,2570,2571,2574],{},"Einen Pfad vergessen, vor allem bei „verschiedene Farben“: rot-blau ",[568,2572,2573],{},"und"," blau-rot gehören dazu.",[582,2576,2577],{},"Die Pfadwahrscheinlichkeiten multiplizieren statt addieren. Multipliziert wird nur entlang eines Pfades.",[582,2579,2580,2581,2691],{},"Bei vielen passenden Pfaden alles einzeln rechnen, obwohl das Gegenereignis nur wenige Pfade hat. Dann ist ",[599,2582,2584,2616],{"className":2583},[602],[599,2585,2587],{"className":2586},[606],[608,2588,2589],{"xmlns":610},[612,2590,2591,2613],{},[615,2592,2593,2595,2598,2600,2602,2611],{},[618,2594,1970],{},[691,2596,2597],{},"−",[687,2599,689],{},[691,2601,694],{"stretchy":693},[2603,2604,2605,2608],"mover",{"accent":629},[687,2606,2607],{},"E",[691,2609,2610],{"stretchy":629},"‾",[691,2612,701],{"stretchy":693},[622,2614,2615],{"encoding":624},"1 - P(\\overline{E})",[599,2617,2619,2638],{"className":2618,"ariaHidden":629},[628],[599,2620,2622,2626,2629,2632,2635],{"className":2621},[633],[599,2623],{"className":2624,"style":2625},[637],"height:0.7278em;vertical-align:-0.0833em;",[599,2627,1970],{"className":2628},[642],[599,2630],{"className":2631,"style":964},[867],[599,2633,2597],{"className":2634},[968],[599,2636],{"className":2637,"style":964},[867],[599,2639,2641,2645,2648,2651,2688],{"className":2640},[633],[599,2642],{"className":2643,"style":2644},[637],"height:1.1333em;vertical-align:-0.25em;",[599,2646,689],{"className":2647,"style":719},[642,718],[599,2649,694],{"className":2650},[723],[599,2652,2655],{"className":2653},[642,2654],"overline",[599,2656,2658],{"className":2657},[896],[599,2659,2661],{"className":2660},[901],[599,2662,2665,2678],{"className":2663,"style":2664},[905],"height:0.8833em;",[599,2666,2668,2671],{"style":2667},"top:-3em;",[599,2669],{"className":2670,"style":914},[913],[599,2672,2674],{"className":2673},[642],[599,2675,2607],{"className":2676,"style":2677},[642,718],"margin-right:0.0576em;",[599,2679,2681,2684],{"style":2680},"top:-3.8033em;",[599,2682],{"className":2683,"style":914},[913],[599,2685],{"className":2686,"style":931},[2687],"overline-line",[599,2689,701],{"className":2690},[734]," schneller.",{"title":2693,"searchDepth":2694,"depth":2694,"links":2695},"",2,[2696,2697,2698],{"id":561,"depth":2694,"text":562},{"id":593,"depth":2694,"text":594},{"id":2563,"depth":2694,"text":2564},[2700,2703,2706,2709,2712,2714],{"lhs":2701,"rhs":2702},"3\u002F8 * 2\u002F7 + 5\u002F8 * 4\u002F7","13\u002F28",{"lhs":2704,"rhs":2705},"6\u002F56 + 20\u002F56","26\u002F56",{"lhs":2707,"rhs":2708},"round(13\u002F28, 3)","0.464",{"lhs":2710,"rhs":2711},"3\u002F8 * 5\u002F7 + 5\u002F8 * 3\u002F7","15\u002F28",{"lhs":2713,"rhs":1970},"13\u002F28 + 15\u002F28",{"lhs":2715,"rhs":2716},"0.7 * 0.2 + 0.3 * 0.6","0.32",null,"md","path-addition-rule","P(E) = P(\\text{Pfad}_1) + P(\\text{Pfad}_2) + \\ldots + P(\\text{Pfad}_m)","\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>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(E) = P(\\text{Pfad}_1) + P(\\text{Pfad}_2) + \\ldots + P(\\text{Pfad}_m)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\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\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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-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=\"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\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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-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=\"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:0.6667em;vertical-align:-0.0833em;\">\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: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\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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-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\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadadditionsregel",[],[2728,2729,2730,2731],"path-multiplication-rule","complement-probability","addition-rule","conditional-probability",{"title":548,"description":2693},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadadditionsregel","Die Wahrscheinlichkeit eines Ereignisses ist die Summe der Wahrscheinlichkeiten aller Pfade, die zu ihm gehören.",[2736,2737,2738,2739],"baumdiagramm","pfadregel","ereignis","wahrscheinlichkeit",[2741,2744,2748,2752],{"symbol":2607,"meaning":2742,"symbolHtml":2743},"Ereignis, das aus mehreren Ergebnissen besteht","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2745,"meaning":2746,"symbolHtml":2747},"P(E)","Wahrscheinlichkeit des Ereignisses","\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>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(E)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2749,"meaning":2750,"symbolHtml":2751},"P(\\text{Pfad}_1), \\ldots, P(\\text{Pfad}_m)","Wahrscheinlichkeiten der Pfade, die zu E gehören (jeweils nach der Pfadmultiplikationsregel)","\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>\u003Cmsub>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmtext>Pfad\u003C\u002Fmtext>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(\\text{Pfad}_1), \\ldots, P(\\text{Pfad}_m)\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\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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-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=\"mclose\">)\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 mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Pfad\u003C\u002Fspan>\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-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\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2753,"meaning":2754,"symbolHtml":2755},"m","Anzahl der Pfade, die zu E gehören","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m\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\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","meDGrrbv6kdXBGPTynAx9gKSHkq1o9k3sVlYJhrklW4",[2758,2761,2764,2767],{"stem":2759,"title":2760,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fadditionssatz","Additionssatz",{"stem":2762,"title":2763,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbedingte-wahrscheinlichkeit","Bedingte Wahrscheinlichkeit",{"stem":2765,"title":2766,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit","Gegenwahrscheinlichkeit",{"stem":2768,"title":2769,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel","Pfadmultiplikationsregel",1793824287047]