[{"data":1,"prerenderedAt":2599},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit":2586},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":441,"checks":2529,"conditions":2547,"conditionsHtml":2547,"deprecated":2547,"description":2523,"extension":2548,"figure":2547,"figureCaption":2547,"figureHtml":2547,"formulaId":2549,"latex":2550,"latexHtml":2551,"level":2552,"meta":2553,"navigation":2554,"path":2555,"redirectFrom":2556,"related":2557,"seo":2562,"stem":2563,"subject":581,"summary":2564,"tags":2565,"variables":2570,"__hash__":2585},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit.md","Gegenwahrscheinlichkeit",[550,551,552,553,554],"Gegenereignis","mindestens einmal Wahrscheinlichkeit","1 minus P","Wahrscheinlichkeit Gegenereignis berechnen","Mindestens-Aufgabe",{"type":556,"value":557,"toc":2522},"minimark",[558,563,939,946,950,1055,1058,1545,1793,2323,2355,2359],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570,571,663,664,693,694,722,723,783,784,938],"p",{},"Das ",[568,569,550],"strong",{}," ",[572,573,576,607],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,602],"semantics",{},[588,589,590],"mrow",{},[591,592,594,598],"mover",{"accent":593},"true",[595,596,597],"mi",{},"A",[599,600,601],"mo",{"stretchy":593},"‾",[603,604,606],"annotation",{"encoding":605},"application\u002Fx-tex","\\overline{A}",[572,608,611],{"className":609,"ariaHidden":593},[610],"katex-html",[572,612,615,620],{"className":613},[614],"base",[572,616],{"className":617,"style":619},[618],"strut","height:0.8833em;",[572,621,625],{"className":622},[623,624],"mord","overline",[572,626,629],{"className":627},[628],"vlist-t",[572,630,633],{"className":631},[632],"vlist-r",[572,634,637,652],{"className":635,"style":619},[636],"vlist",[572,638,640,645],{"style":639},"top:-3em;",[572,641],{"className":642,"style":644},[643],"pstrut","height:3em;",[572,646,648],{"className":647},[623],[572,649,597],{"className":650},[623,651],"mathnormal",[572,653,655,658],{"style":654},"top:-3.8033em;",[572,656],{"className":657,"style":644},[643],[572,659],{"className":660,"style":662},[661],"overline-line","border-bottom-width:0.04em;"," tritt genau dann ein, wenn ",[572,665,667,680],{"className":666},[575],[572,668,670],{"className":669},[579],[581,671,672],{"xmlns":583},[585,673,674,678],{},[588,675,676],{},[595,677,597],{},[603,679,597],{"encoding":605},[572,681,683],{"className":682,"ariaHidden":593},[610],[572,684,686,690],{"className":685},[614],[572,687],{"className":688,"style":689},[618],"height:0.6833em;",[572,691,597],{"className":692},[623,651]," nicht eintritt. ",[572,695,697,710],{"className":696},[575],[572,698,700],{"className":699},[579],[581,701,702],{"xmlns":583},[585,703,704,708],{},[588,705,706],{},[595,707,597],{},[603,709,597],{"encoding":605},[572,711,713],{"className":712,"ariaHidden":593},[610],[572,714,716,719],{"className":715},[614],[572,717],{"className":718,"style":689},[618],[572,720,597],{"className":721},[623,651]," und ",[572,724,726,743],{"className":725},[575],[572,727,729],{"className":728},[579],[581,730,731],{"xmlns":583},[585,732,733,741],{},[588,734,735],{},[591,736,737,739],{"accent":593},[595,738,597],{},[599,740,601],{"stretchy":593},[603,742,606],{"encoding":605},[572,744,746],{"className":745,"ariaHidden":593},[610],[572,747,749,752],{"className":748},[614],[572,750],{"className":751,"style":619},[618],[572,753,755],{"className":754},[623,624],[572,756,758],{"className":757},[628],[572,759,761],{"className":760},[632],[572,762,764,775],{"className":763,"style":619},[636],[572,765,766,769],{"style":639},[572,767],{"className":768,"style":644},[643],[572,770,772],{"className":771},[623],[572,773,597],{"className":774},[623,651],[572,776,777,780],{"style":654},[572,778],{"className":779,"style":644},[643],[572,781],{"className":782,"style":662},[661]," zusammen decken alle Ergebnisse ab, deshalb gilt ",[572,785,787,833],{"className":786},[575],[572,788,790],{"className":789},[579],[581,791,792],{"xmlns":583},[585,793,794,830],{},[588,795,796,799,803,805,808,811,813,815,821,823,826],{},[595,797,798],{},"P",[599,800,802],{"stretchy":801},"false","(",[595,804,597],{},[599,806,807],{"stretchy":801},")",[599,809,810],{},"+",[595,812,798],{},[599,814,802],{"stretchy":801},[591,816,817,819],{"accent":593},[595,818,597],{},[599,820,601],{"stretchy":593},[599,822,807],{"stretchy":801},[599,824,825],{},"=",[827,828,829],"mn",{},"1",[603,831,832],{"encoding":605},"P(A) + P(\\overline{A}) = 1",[572,834,836,870,928],{"className":835,"ariaHidden":593},[610],[572,837,839,843,847,851,854,858,863,867],{"className":838},[614],[572,840],{"className":841,"style":842},[618],"height:1em;vertical-align:-0.25em;",[572,844,798],{"className":845,"style":846},[623,651],"margin-right:0.1389em;",[572,848,802],{"className":849},[850],"mopen",[572,852,597],{"className":853},[623,651],[572,855,807],{"className":856},[857],"mclose",[572,859],{"className":860,"style":862},[861],"mspace","margin-right:0.2222em;",[572,864,810],{"className":865},[866],"mbin",[572,868],{"className":869,"style":862},[861],[572,871,873,877,880,883,914,917,921,925],{"className":872},[614],[572,874],{"className":875,"style":876},[618],"height:1.1333em;vertical-align:-0.25em;",[572,878,798],{"className":879,"style":846},[623,651],[572,881,802],{"className":882},[850],[572,884,886],{"className":885},[623,624],[572,887,889],{"className":888},[628],[572,890,892],{"className":891},[632],[572,893,895,906],{"className":894,"style":619},[636],[572,896,897,900],{"style":639},[572,898],{"className":899,"style":644},[643],[572,901,903],{"className":902},[623],[572,904,597],{"className":905},[623,651],[572,907,908,911],{"style":654},[572,909],{"className":910,"style":644},[643],[572,912],{"className":913,"style":662},[661],[572,915,807],{"className":916},[857],[572,918],{"className":919,"style":920},[861],"margin-right:0.2778em;",[572,922,825],{"className":923},[924],"mrel",[572,926],{"className":927,"style":920},[861],[572,929,931,935],{"className":930},[614],[572,932],{"className":933,"style":934},[618],"height:0.6444em;",[572,936,829],{"className":937},[623],".",[564,940,941,942,945],{},"Die Formel spart viel Arbeit, wenn das Gegenereignis einfacher zu berechnen ist. Das typische Signal ist das Wort ",[568,943,944],{},"„mindestens einmal“",": Das Gegenereignis ist dann „kein einziges Mal“, und dafür gibt es nur einen Pfad im Baumdiagramm.",[559,947,949],{"id":948},"beispiele","Beispiele",[564,951,952,953,1054],{},"Die Regenwahrscheinlichkeit für morgen liegt bei 30 %. Dann bleibt es mit ",[572,954,956,981],{"className":955},[575],[572,957,959],{"className":958},[579],[581,960,961],{"xmlns":583},[585,962,963,978],{},[588,964,965,967,970,973,975],{},[827,966,829],{},[599,968,969],{},"−",[827,971,972],{},"0,3",[599,974,825],{},[827,976,977],{},"0,7",[603,979,980],{"encoding":605},"1 - 0{,}3 = 0{,}7",[572,982,984,1003,1035],{"className":983,"ariaHidden":593},[610],[572,985,987,991,994,997,1000],{"className":986},[614],[572,988],{"className":989,"style":990},[618],"height:0.7278em;vertical-align:-0.0833em;",[572,992,829],{"className":993},[623],[572,995],{"className":996,"style":862},[861],[572,998,969],{"className":999},[866],[572,1001],{"className":1002,"style":862},[861],[572,1004,1006,1010,1014,1022,1026,1029,1032],{"className":1005},[614],[572,1007],{"className":1008,"style":1009},[618],"height:0.8389em;vertical-align:-0.1944em;",[572,1011,1013],{"className":1012},[623],"0",[572,1015,1017],{"className":1016},[623],[572,1018,1021],{"className":1019},[1020],"mpunct",",",[572,1023,1025],{"className":1024},[623],"3",[572,1027],{"className":1028,"style":920},[861],[572,1030,825],{"className":1031},[924],[572,1033],{"className":1034,"style":920},[861],[572,1036,1038,1041,1044,1050],{"className":1037},[614],[572,1039],{"className":1040,"style":1009},[618],[572,1042,1013],{"className":1043},[623],[572,1045,1047],{"className":1046},[623],[572,1048,1021],{"className":1049},[1020],[572,1051,1053],{"className":1052},[623],"7",", also 70 %, trocken.",[564,1056,1057],{},"Ein Würfel wird viermal geworfen. Gesucht ist die Wahrscheinlichkeit für mindestens eine Sechs. Das Gegenereignis ist „keine Sechs in vier Würfen“:",[572,1059,1062],{"className":1060},[1061],"katex-display",[572,1063,1065,1151],{"className":1064},[575],[572,1066,1068],{"className":1067},[579],[581,1069,1071],{"xmlns":583,"display":1070},"block",[585,1072,1073,1148],{},[588,1074,1075,1077,1079,1083,1085,1087,1089,1091,1112,1114,1116,1118,1126,1128,1135,1138,1141,1144],{},[595,1076,798],{},[599,1078,802],{"stretchy":801},[1080,1081,1082],"mtext",{},"mind. eine Sechs",[599,1084,807],{"stretchy":801},[599,1086,825],{},[827,1088,829],{},[599,1090,969],{},[1092,1093,1094,1109],"msup",{},[588,1095,1096,1098,1107],{},[599,1097,802],{"fence":593},[1099,1100,1101,1104],"mfrac",{},[827,1102,1103],{},"5",[827,1105,1106],{},"6",[599,1108,807],{"fence":593},[827,1110,1111],{},"4",[599,1113,825],{},[827,1115,829],{},[599,1117,969],{},[1099,1119,1120,1123],{},[827,1121,1122],{},"625",[827,1124,1125],{},"1296",[599,1127,825],{},[1099,1129,1130,1133],{},[827,1131,1132],{},"671",[827,1134,1125],{},[599,1136,1137],{},"≈",[827,1139,1140],{},"51,8",[1080,1142,1143],{}," ",[595,1145,1147],{"mathvariant":1146},"normal","%",[603,1149,1150],{"encoding":605},"P(\\text{mind. eine Sechs}) = 1 - \\left(\\frac{5}{6}\\right)^4 = 1 - \\frac{625}{1296} = \\frac{671}{1296} \\approx 51{,}8\\,\\%",[572,1152,1154,1185,1203,1344,1362,1440,1517],{"className":1153,"ariaHidden":593},[610],[572,1155,1157,1160,1163,1166,1173,1176,1179,1182],{"className":1156},[614],[572,1158],{"className":1159,"style":842},[618],[572,1161,798],{"className":1162,"style":846},[623,651],[572,1164,802],{"className":1165},[850],[572,1167,1170],{"className":1168},[623,1169],"text",[572,1171,1082],{"className":1172},[623],[572,1174,807],{"className":1175},[857],[572,1177],{"className":1178,"style":920},[861],[572,1180,825],{"className":1181},[924],[572,1183],{"className":1184,"style":920},[861],[572,1186,1188,1191,1194,1197,1200],{"className":1187},[614],[572,1189],{"className":1190,"style":990},[618],[572,1192,829],{"className":1193},[623],[572,1195],{"className":1196,"style":862},[861],[572,1198,969],{"className":1199},[866],[572,1201],{"className":1202,"style":862},[861],[572,1204,1206,1210,1335,1338,1341],{"className":1205},[614],[572,1207],{"className":1208,"style":1209},[618],"height:2.604em;vertical-align:-0.95em;",[572,1211,1214,1305],{"className":1212},[1213],"minner",[572,1215,1217,1227,1299],{"className":1216},[1213],[572,1218,1222],{"className":1219,"style":1221},[850,1220],"delimcenter","top:0em;",[572,1223,802],{"className":1224},[1225,1226],"delimsizing","size3",[572,1228,1230,1234,1296],{"className":1229},[623],[572,1231],{"className":1232},[850,1233],"nulldelimiter",[572,1235,1237],{"className":1236},[1099],[572,1238,1241,1287],{"className":1239},[628,1240],"vlist-t2",[572,1242,1244,1282],{"className":1243},[632],[572,1245,1248,1260,1270],{"className":1246,"style":1247},[636],"height:1.3214em;",[572,1249,1251,1254],{"style":1250},"top:-2.314em;",[572,1252],{"className":1253,"style":644},[643],[572,1255,1257],{"className":1256},[623],[572,1258,1106],{"className":1259},[623],[572,1261,1263,1266],{"style":1262},"top:-3.23em;",[572,1264],{"className":1265,"style":644},[643],[572,1267],{"className":1268,"style":662},[1269],"frac-line",[572,1271,1273,1276],{"style":1272},"top:-3.677em;",[572,1274],{"className":1275,"style":644},[643],[572,1277,1279],{"className":1278},[623],[572,1280,1103],{"className":1281},[623],[572,1283,1286],{"className":1284},[1285],"vlist-s","​",[572,1288,1290],{"className":1289},[632],[572,1291,1294],{"className":1292,"style":1293},[636],"height:0.686em;",[572,1295],{},[572,1297],{"className":1298},[857,1233],[572,1300,1302],{"className":1301,"style":1221},[857,1220],[572,1303,807],{"className":1304},[1225,1226],[572,1306,1309],{"className":1307},[1308],"msupsub",[572,1310,1312],{"className":1311},[628],[572,1313,1315],{"className":1314},[632],[572,1316,1319],{"className":1317,"style":1318},[636],"height:1.654em;",[572,1320,1322,1326],{"style":1321},"top:-3.9029em;margin-right:0.05em;",[572,1323],{"className":1324,"style":1325},[643],"height:2.7em;",[572,1327,1332],{"className":1328},[1329,1330,1226,1331],"sizing","reset-size6","mtight",[572,1333,1111],{"className":1334},[623,1331],[572,1336],{"className":1337,"style":920},[861],[572,1339,825],{"className":1340},[924],[572,1342],{"className":1343,"style":920},[861],[572,1345,1347,1350,1353,1356,1359],{"className":1346},[614],[572,1348],{"className":1349,"style":990},[618],[572,1351,829],{"className":1352},[623],[572,1354],{"className":1355,"style":862},[861],[572,1357,969],{"className":1358},[866],[572,1360],{"className":1361,"style":862},[861],[572,1363,1365,1369,1431,1434,1437],{"className":1364},[614],[572,1366],{"className":1367,"style":1368},[618],"height:2.0074em;vertical-align:-0.686em;",[572,1370,1372,1375,1428],{"className":1371},[623],[572,1373],{"className":1374},[850,1233],[572,1376,1378],{"className":1377},[1099],[572,1379,1381,1420],{"className":1380},[628,1240],[572,1382,1384,1417],{"className":1383},[632],[572,1385,1387,1398,1406],{"className":1386,"style":1247},[636],[572,1388,1389,1392],{"style":1250},[572,1390],{"className":1391,"style":644},[643],[572,1393,1395],{"className":1394},[623],[572,1396,1125],{"className":1397},[623],[572,1399,1400,1403],{"style":1262},[572,1401],{"className":1402,"style":644},[643],[572,1404],{"className":1405,"style":662},[1269],[572,1407,1408,1411],{"style":1272},[572,1409],{"className":1410,"style":644},[643],[572,1412,1414],{"className":1413},[623],[572,1415,1122],{"className":1416},[623],[572,1418,1286],{"className":1419},[1285],[572,1421,1423],{"className":1422},[632],[572,1424,1426],{"className":1425,"style":1293},[636],[572,1427],{},[572,1429],{"className":1430},[857,1233],[572,1432],{"className":1433,"style":920},[861],[572,1435,825],{"className":1436},[924],[572,1438],{"className":1439,"style":920},[861],[572,1441,1443,1446,1508,1511,1514],{"className":1442},[614],[572,1444],{"className":1445,"style":1368},[618],[572,1447,1449,1452,1505],{"className":1448},[623],[572,1450],{"className":1451},[850,1233],[572,1453,1455],{"className":1454},[1099],[572,1456,1458,1497],{"className":1457},[628,1240],[572,1459,1461,1494],{"className":1460},[632],[572,1462,1464,1475,1483],{"className":1463,"style":1247},[636],[572,1465,1466,1469],{"style":1250},[572,1467],{"className":1468,"style":644},[643],[572,1470,1472],{"className":1471},[623],[572,1473,1125],{"className":1474},[623],[572,1476,1477,1480],{"style":1262},[572,1478],{"className":1479,"style":644},[643],[572,1481],{"className":1482,"style":662},[1269],[572,1484,1485,1488],{"style":1272},[572,1486],{"className":1487,"style":644},[643],[572,1489,1491],{"className":1490},[623],[572,1492,1132],{"className":1493},[623],[572,1495,1286],{"className":1496},[1285],[572,1498,1500],{"className":1499},[632],[572,1501,1503],{"className":1502,"style":1293},[636],[572,1504],{},[572,1506],{"className":1507},[857,1233],[572,1509],{"className":1510,"style":920},[861],[572,1512,1137],{"className":1513},[924],[572,1515],{"className":1516,"style":920},[861],[572,1518,1520,1524,1528,1534,1538,1542],{"className":1519},[614],[572,1521],{"className":1522,"style":1523},[618],"height:0.9444em;vertical-align:-0.1944em;",[572,1525,1527],{"className":1526},[623],"51",[572,1529,1531],{"className":1530},[623],[572,1532,1021],{"className":1533},[1020],[572,1535,1537],{"className":1536},[623],"8",[572,1539],{"className":1540,"style":1541},[861],"margin-right:0.1667em;",[572,1543,1147],{"className":1544},[623],[564,1546,1547,1548,1578,1579,1792],{},"Wie oft muss man würfeln, damit mit mindestens 90 % Wahrscheinlichkeit eine Sechs dabei ist? Gesucht ist das kleinste ",[572,1549,1551,1565],{"className":1550},[575],[572,1552,1554],{"className":1553},[579],[581,1555,1556],{"xmlns":583},[585,1557,1558,1563],{},[588,1559,1560],{},[595,1561,1562],{},"n",[603,1564,1562],{"encoding":605},[572,1566,1568],{"className":1567,"ariaHidden":593},[610],[572,1569,1571,1575],{"className":1570},[614],[572,1572],{"className":1573,"style":1574},[618],"height:0.4306em;",[572,1576,1562],{"className":1577},[623,651]," mit ",[572,1580,1582,1620],{"className":1581},[575],[572,1583,1585],{"className":1584},[579],[581,1586,1587],{"xmlns":583},[585,1588,1589,1617],{},[588,1590,1591,1593,1595,1611,1614],{},[827,1592,829],{},[599,1594,969],{},[1092,1596,1597,1609],{},[588,1598,1599,1601,1607],{},[599,1600,802],{"fence":593},[1099,1602,1603,1605],{},[827,1604,1103],{},[827,1606,1106],{},[599,1608,807],{"fence":593},[595,1610,1562],{},[599,1612,1613],{},"≥",[827,1615,1616],{},"0,9",[603,1618,1619],{"encoding":605},"1 - \\left(\\frac{5}{6}\\right)^n \\geq 0{,}9",[572,1621,1623,1641,1773],{"className":1622,"ariaHidden":593},[610],[572,1624,1626,1629,1632,1635,1638],{"className":1625},[614],[572,1627],{"className":1628,"style":990},[618],[572,1630,829],{"className":1631},[623],[572,1633],{"className":1634,"style":862},[861],[572,1636,969],{"className":1637},[866],[572,1639],{"className":1640,"style":862},[861],[572,1642,1644,1648,1764,1767,1770],{"className":1643},[614],[572,1645],{"className":1646,"style":1647},[618],"height:1.2543em;vertical-align:-0.35em;",[572,1649,1651,1739],{"className":1650},[1213],[572,1652,1654,1661,1733],{"className":1653},[1213],[572,1655,1657],{"className":1656,"style":1221},[850,1220],[572,1658,802],{"className":1659},[1225,1660],"size1",[572,1662,1664,1667,1730],{"className":1663},[623],[572,1665],{"className":1666},[850,1233],[572,1668,1670],{"className":1669},[1099],[572,1671,1673,1721],{"className":1672},[628,1240],[572,1674,1676,1718],{"className":1675},[632],[572,1677,1680,1695,1703],{"className":1678,"style":1679},[636],"height:0.8451em;",[572,1681,1683,1686],{"style":1682},"top:-2.655em;",[572,1684],{"className":1685,"style":644},[643],[572,1687,1689],{"className":1688},[1329,1330,1226,1331],[572,1690,1692],{"className":1691},[623,1331],[572,1693,1106],{"className":1694},[623,1331],[572,1696,1697,1700],{"style":1262},[572,1698],{"className":1699,"style":644},[643],[572,1701],{"className":1702,"style":662},[1269],[572,1704,1706,1709],{"style":1705},"top:-3.394em;",[572,1707],{"className":1708,"style":644},[643],[572,1710,1712],{"className":1711},[1329,1330,1226,1331],[572,1713,1715],{"className":1714},[623,1331],[572,1716,1103],{"className":1717},[623,1331],[572,1719,1286],{"className":1720},[1285],[572,1722,1724],{"className":1723},[632],[572,1725,1728],{"className":1726,"style":1727},[636],"height:0.345em;",[572,1729],{},[572,1731],{"className":1732},[857,1233],[572,1734,1736],{"className":1735,"style":1221},[857,1220],[572,1737,807],{"className":1738},[1225,1660],[572,1740,1742],{"className":1741},[1308],[572,1743,1745],{"className":1744},[628],[572,1746,1748],{"className":1747},[632],[572,1749,1752],{"className":1750,"style":1751},[636],"height:0.9043em;",[572,1753,1755,1758],{"style":1754},"top:-3.3029em;margin-right:0.05em;",[572,1756],{"className":1757,"style":1325},[643],[572,1759,1761],{"className":1760},[1329,1330,1226,1331],[572,1762,1562],{"className":1763},[623,651,1331],[572,1765],{"className":1766,"style":920},[861],[572,1768,1613],{"className":1769},[924],[572,1771],{"className":1772,"style":920},[861],[572,1774,1776,1779,1782,1788],{"className":1775},[614],[572,1777],{"className":1778,"style":1009},[618],[572,1780,1013],{"className":1781},[623],[572,1783,1785],{"className":1784},[623],[572,1786,1021],{"className":1787},[1020],[572,1789,1791],{"className":1790},[623],"9",". Probieren ergibt:",[1794,1795,1796,2062],"ul",{},[1797,1798,1799,1851,1852,2061],"li",{},[572,1800,1802,1821],{"className":1801},[575],[572,1803,1805],{"className":1804},[579],[581,1806,1807],{"xmlns":583},[585,1808,1809,1818],{},[588,1810,1811,1813,1815],{},[595,1812,1562],{},[599,1814,825],{},[827,1816,1817],{},"12",[603,1819,1820],{"encoding":605},"n = 12",[572,1822,1824,1842],{"className":1823,"ariaHidden":593},[610],[572,1825,1827,1830,1833,1836,1839],{"className":1826},[614],[572,1828],{"className":1829,"style":1574},[618],[572,1831,1562],{"className":1832},[623,651],[572,1834],{"className":1835,"style":920},[861],[572,1837,825],{"className":1838},[924],[572,1840],{"className":1841,"style":920},[861],[572,1843,1845,1848],{"className":1844},[614],[572,1846],{"className":1847,"style":934},[618],[572,1849,1817],{"className":1850},[623],": ",[572,1853,1855,1892],{"className":1854},[575],[572,1856,1858],{"className":1857},[579],[581,1859,1860],{"xmlns":583},[585,1861,1862,1889],{},[588,1863,1864,1866,1868,1884,1886],{},[827,1865,829],{},[599,1867,969],{},[1092,1869,1870,1882],{},[588,1871,1872,1874,1880],{},[599,1873,802],{"fence":593},[1099,1875,1876,1878],{},[827,1877,1103],{},[827,1879,1106],{},[599,1881,807],{"fence":593},[827,1883,1817],{},[599,1885,1137],{},[827,1887,1888],{},"0,8878",[603,1890,1891],{"encoding":605},"1 - \\left(\\frac{5}{6}\\right)^{12} \\approx 0{,}8878",[572,1893,1895,1913,2042],{"className":1894,"ariaHidden":593},[610],[572,1896,1898,1901,1904,1907,1910],{"className":1897},[614],[572,1899],{"className":1900,"style":990},[618],[572,1902,829],{"className":1903},[623],[572,1905],{"className":1906,"style":862},[861],[572,1908,969],{"className":1909},[866],[572,1911],{"className":1912,"style":862},[861],[572,1914,1916,1920,2033,2036,2039],{"className":1915},[614],[572,1917],{"className":1918,"style":1919},[618],"height:1.404em;vertical-align:-0.35em;",[572,1921,1923,2006],{"className":1922},[1213],[572,1924,1926,1932,2000],{"className":1925},[1213],[572,1927,1929],{"className":1928,"style":1221},[850,1220],[572,1930,802],{"className":1931},[1225,1660],[572,1933,1935,1938,1997],{"className":1934},[623],[572,1936],{"className":1937},[850,1233],[572,1939,1941],{"className":1940},[1099],[572,1942,1944,1989],{"className":1943},[628,1240],[572,1945,1947,1986],{"className":1946},[632],[572,1948,1950,1964,1972],{"className":1949,"style":1679},[636],[572,1951,1952,1955],{"style":1682},[572,1953],{"className":1954,"style":644},[643],[572,1956,1958],{"className":1957},[1329,1330,1226,1331],[572,1959,1961],{"className":1960},[623,1331],[572,1962,1106],{"className":1963},[623,1331],[572,1965,1966,1969],{"style":1262},[572,1967],{"className":1968,"style":644},[643],[572,1970],{"className":1971,"style":662},[1269],[572,1973,1974,1977],{"style":1705},[572,1975],{"className":1976,"style":644},[643],[572,1978,1980],{"className":1979},[1329,1330,1226,1331],[572,1981,1983],{"className":1982},[623,1331],[572,1984,1103],{"className":1985},[623,1331],[572,1987,1286],{"className":1988},[1285],[572,1990,1992],{"className":1991},[632],[572,1993,1995],{"className":1994,"style":1727},[636],[572,1996],{},[572,1998],{"className":1999},[857,1233],[572,2001,2003],{"className":2002,"style":1221},[857,1220],[572,2004,807],{"className":2005},[1225,1660],[572,2007,2009],{"className":2008},[1308],[572,2010,2012],{"className":2011},[628],[572,2013,2015],{"className":2014},[632],[572,2016,2019],{"className":2017,"style":2018},[636],"height:1.054em;",[572,2020,2021,2024],{"style":1754},[572,2022],{"className":2023,"style":1325},[643],[572,2025,2027],{"className":2026},[1329,1330,1226,1331],[572,2028,2030],{"className":2029},[623,1331],[572,2031,1817],{"className":2032},[623,1331],[572,2034],{"className":2035,"style":920},[861],[572,2037,1137],{"className":2038},[924],[572,2040],{"className":2041,"style":920},[861],[572,2043,2045,2048,2051,2057],{"className":2044},[614],[572,2046],{"className":2047,"style":1009},[618],[572,2049,1013],{"className":2050},[623],[572,2052,2054],{"className":2053},[623],[572,2055,1021],{"className":2056},[1020],[572,2058,2060],{"className":2059},[623],"8878",", das reicht noch nicht.",[1797,2063,2064,1851,2116,938],{},[572,2065,2067,2086],{"className":2066},[575],[572,2068,2070],{"className":2069},[579],[581,2071,2072],{"xmlns":583},[585,2073,2074,2083],{},[588,2075,2076,2078,2080],{},[595,2077,1562],{},[599,2079,825],{},[827,2081,2082],{},"13",[603,2084,2085],{"encoding":605},"n = 13",[572,2087,2089,2107],{"className":2088,"ariaHidden":593},[610],[572,2090,2092,2095,2098,2101,2104],{"className":2091},[614],[572,2093],{"className":2094,"style":1574},[618],[572,2096,1562],{"className":2097},[623,651],[572,2099],{"className":2100,"style":920},[861],[572,2102,825],{"className":2103},[924],[572,2105],{"className":2106,"style":920},[861],[572,2108,2110,2113],{"className":2109},[614],[572,2111],{"className":2112,"style":934},[618],[572,2114,2082],{"className":2115},[623],[572,2117,2119,2156],{"className":2118},[575],[572,2120,2122],{"className":2121},[579],[581,2123,2124],{"xmlns":583},[585,2125,2126,2153],{},[588,2127,2128,2130,2132,2148,2150],{},[827,2129,829],{},[599,2131,969],{},[1092,2133,2134,2146],{},[588,2135,2136,2138,2144],{},[599,2137,802],{"fence":593},[1099,2139,2140,2142],{},[827,2141,1103],{},[827,2143,1106],{},[599,2145,807],{"fence":593},[827,2147,2082],{},[599,2149,1137],{},[827,2151,2152],{},"0,9065",[603,2154,2155],{"encoding":605},"1 - \\left(\\frac{5}{6}\\right)^{13} \\approx 0{,}9065",[572,2157,2159,2177,2304],{"className":2158,"ariaHidden":593},[610],[572,2160,2162,2165,2168,2171,2174],{"className":2161},[614],[572,2163],{"className":2164,"style":990},[618],[572,2166,829],{"className":2167},[623],[572,2169],{"className":2170,"style":862},[861],[572,2172,969],{"className":2173},[866],[572,2175],{"className":2176,"style":862},[861],[572,2178,2180,2183,2295,2298,2301],{"className":2179},[614],[572,2181],{"className":2182,"style":1919},[618],[572,2184,2186,2269],{"className":2185},[1213],[572,2187,2189,2195,2263],{"className":2188},[1213],[572,2190,2192],{"className":2191,"style":1221},[850,1220],[572,2193,802],{"className":2194},[1225,1660],[572,2196,2198,2201,2260],{"className":2197},[623],[572,2199],{"className":2200},[850,1233],[572,2202,2204],{"className":2203},[1099],[572,2205,2207,2252],{"className":2206},[628,1240],[572,2208,2210,2249],{"className":2209},[632],[572,2211,2213,2227,2235],{"className":2212,"style":1679},[636],[572,2214,2215,2218],{"style":1682},[572,2216],{"className":2217,"style":644},[643],[572,2219,2221],{"className":2220},[1329,1330,1226,1331],[572,2222,2224],{"className":2223},[623,1331],[572,2225,1106],{"className":2226},[623,1331],[572,2228,2229,2232],{"style":1262},[572,2230],{"className":2231,"style":644},[643],[572,2233],{"className":2234,"style":662},[1269],[572,2236,2237,2240],{"style":1705},[572,2238],{"className":2239,"style":644},[643],[572,2241,2243],{"className":2242},[1329,1330,1226,1331],[572,2244,2246],{"className":2245},[623,1331],[572,2247,1103],{"className":2248},[623,1331],[572,2250,1286],{"className":2251},[1285],[572,2253,2255],{"className":2254},[632],[572,2256,2258],{"className":2257,"style":1727},[636],[572,2259],{},[572,2261],{"className":2262},[857,1233],[572,2264,2266],{"className":2265,"style":1221},[857,1220],[572,2267,807],{"className":2268},[1225,1660],[572,2270,2272],{"className":2271},[1308],[572,2273,2275],{"className":2274},[628],[572,2276,2278],{"className":2277},[632],[572,2279,2281],{"className":2280,"style":2018},[636],[572,2282,2283,2286],{"style":1754},[572,2284],{"className":2285,"style":1325},[643],[572,2287,2289],{"className":2288},[1329,1330,1226,1331],[572,2290,2292],{"className":2291},[623,1331],[572,2293,2082],{"className":2294},[623,1331],[572,2296],{"className":2297,"style":920},[861],[572,2299,1137],{"className":2300},[924],[572,2302],{"className":2303,"style":920},[861],[572,2305,2307,2310,2313,2319],{"className":2306},[614],[572,2308],{"className":2309,"style":1009},[618],[572,2311,1013],{"className":2312},[623],[572,2314,2316],{"className":2315},[623],[572,2317,1021],{"className":2318},[1020],[572,2320,2322],{"className":2321},[623],"9065",[564,2324,2325,2326,2354],{},"Man muss also mindestens ",[572,2327,2329,2342],{"className":2328},[575],[572,2330,2332],{"className":2331},[579],[581,2333,2334],{"xmlns":583},[585,2335,2336,2340],{},[588,2337,2338],{},[827,2339,2082],{},[603,2341,2082],{"encoding":605},[572,2343,2345],{"className":2344,"ariaHidden":593},[610],[572,2346,2348,2351],{"className":2347},[614],[572,2349],{"className":2350,"style":934},[618],[572,2352,2082],{"className":2353},[623],"-mal würfeln.",[559,2356,2358],{"id":2357},"typische-fehler","Typische Fehler",[1794,2360,2361,2364,2367],{},[1797,2362,2363],{},"Das falsche Gegenereignis bilden: Das Gegenteil von „mindestens eine Sechs“ ist „keine Sechs“, nicht „höchstens eine Sechs“.",[1797,2365,2366],{},"Das Gegenteil von „genau zwei Treffer“ ist nicht „null Treffer“, sondern „0, 1, 3, 4, … Treffer“. Die Gegenwahrscheinlichkeit hilft nur, wenn das Gegenereignis weniger Fälle hat als das Ereignis.",[1797,2368,2369,2370,2492,2493,2521],{},"„Mindestens eine Sechs in vier Würfen“ als ",[572,2371,2373,2396],{"className":2372},[575],[572,2374,2376],{"className":2375},[579],[581,2377,2378],{"xmlns":583},[585,2379,2380,2393],{},[588,2381,2382,2384,2387],{},[827,2383,1111],{},[599,2385,2386],{},"⋅",[1099,2388,2389,2391],{},[827,2390,829],{},[827,2392,1106],{},[603,2394,2395],{"encoding":605},"4 \\cdot \\frac{1}{6}",[572,2397,2399,2417],{"className":2398,"ariaHidden":593},[610],[572,2400,2402,2405,2408,2411,2414],{"className":2401},[614],[572,2403],{"className":2404,"style":934},[618],[572,2406,1111],{"className":2407},[623],[572,2409],{"className":2410,"style":862},[861],[572,2412,2386],{"className":2413},[866],[572,2415],{"className":2416,"style":862},[861],[572,2418,2420,2424],{"className":2419},[614],[572,2421],{"className":2422,"style":2423},[618],"height:1.1901em;vertical-align:-0.345em;",[572,2425,2427,2430,2489],{"className":2426},[623],[572,2428],{"className":2429},[850,1233],[572,2431,2433],{"className":2432},[1099],[572,2434,2436,2481],{"className":2435},[628,1240],[572,2437,2439,2478],{"className":2438},[632],[572,2440,2442,2456,2464],{"className":2441,"style":1679},[636],[572,2443,2444,2447],{"style":1682},[572,2445],{"className":2446,"style":644},[643],[572,2448,2450],{"className":2449},[1329,1330,1226,1331],[572,2451,2453],{"className":2452},[623,1331],[572,2454,1106],{"className":2455},[623,1331],[572,2457,2458,2461],{"style":1262},[572,2459],{"className":2460,"style":644},[643],[572,2462],{"className":2463,"style":662},[1269],[572,2465,2466,2469],{"style":1705},[572,2467],{"className":2468,"style":644},[643],[572,2470,2472],{"className":2471},[1329,1330,1226,1331],[572,2473,2475],{"className":2474},[623,1331],[572,2476,829],{"className":2477},[623,1331],[572,2479,1286],{"className":2480},[1285],[572,2482,2484],{"className":2483},[632],[572,2485,2487],{"className":2486,"style":1727},[636],[572,2488],{},[572,2490],{"className":2491},[857,1233]," rechnen. Das zählt Würfe mit mehreren Sechsen mehrfach; bei sieben Würfen käme sogar mehr als ",[572,2494,2496,2509],{"className":2495},[575],[572,2497,2499],{"className":2498},[579],[581,2500,2501],{"xmlns":583},[585,2502,2503,2507],{},[588,2504,2505],{},[827,2506,829],{},[603,2508,829],{"encoding":605},[572,2510,2512],{"className":2511,"ariaHidden":593},[610],[572,2513,2515,2518],{"className":2514},[614],[572,2516],{"className":2517,"style":934},[618],[572,2519,829],{"className":2520},[623]," heraus.",{"title":2523,"searchDepth":2524,"depth":2524,"links":2525},"",2,[2526,2527,2528],{"id":561,"depth":2524,"text":562},{"id":948,"depth":2524,"text":949},{"id":2357,"depth":2524,"text":2358},[2530,2532,2535,2538,2541,2544],{"lhs":2531,"rhs":829},"p + (1 - p)",{"lhs":2533,"rhs":2534},"1 - 0.3","0.7",{"lhs":2536,"rhs":2537},"1 - (5\u002F6)^4","671\u002F1296",{"lhs":2539,"rhs":2540},"round((1 - (5\u002F6)^4) * 100, 1)","51.8",{"lhs":2542,"rhs":2543},"round(1 - (5\u002F6)^12, 4)","0.8878",{"lhs":2545,"rhs":2546},"round(1 - (5\u002F6)^13, 4)","0.9065",null,"md","complement-probability","P(\\overline{A}) = 1 - P(A)","\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>\u003Cmover accent=\"true\">\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(\\overline{A}) = 1 - P(A)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1333em;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 katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit",[],[2558,2559,2560,2561],"laplace-probability","path-multiplication-rule","binomial-distribution","addition-rule",{"title":548,"description":2523},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit","Die Wahrscheinlichkeit, dass ein Ereignis nicht eintritt, ist 1 minus die Wahrscheinlichkeit des Ereignisses.",[2566,2567,2568,2569],"gegenereignis","wahrscheinlichkeit","mindestens einmal","komplement",[2571,2574,2577,2581],{"symbol":597,"meaning":2572,"symbolHtml":2573},"ein Ereignis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\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\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":606,"meaning":2575,"symbolHtml":2576},"Gegenereignis, „A tritt nicht ein“","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{A}\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:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2578,"meaning":2579,"symbolHtml":2580},"P(A)","Wahrscheinlichkeit von A","\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(A)\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2582,"meaning":2583,"symbolHtml":2584},"P(\\overline{A})","Wahrscheinlichkeit des Gegenereignisses","\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>\u003Cmover accent=\"true\">\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(\\overline{A})\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1333em;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 katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Jmm32jUlCG_bIFudlpC7prSAaBDphc3j9jj2JTazWDs",[2587,2590,2593,2596],{"stem":2588,"title":2589,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fadditionssatz","Additionssatz",{"stem":2591,"title":2592,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":2594,"title":2595,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Flaplace-wahrscheinlichkeit","Laplace-Wahrscheinlichkeit",{"stem":2597,"title":2598,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpfadmultiplikationsregel","Pfadmultiplikationsregel",1793824285547]