[{"data":1,"prerenderedAt":2229},["ShallowReactive",2],{"blog-post-es-fundamentos-de-probabilidad":3,"locale-switcher-blog-es-fundamentos-de-probabilidad":2226,"blog-siblings-es-fundamentos-de-probabilidad":2228},{"id":4,"title":5,"_locale":6,"body":7,"date":2205,"description":2206,"extension":2207,"meta":2208,"navigation":2221,"path":2222,"published":2221,"seo":2223,"slug":13,"stem":2224,"__hash__":2225},"blog\u002Fblog\u002Fprobability-basics.es.md","Fundamentos de probabilidad","es",{"type":8,"value":9,"toc":2190},"minimal",[10,14,27,30,35,186,197,201,204,231,234,238,245,263,274,278,289,425,428,870,881,885,888,893,904,1256,1360,1364,1378,1901,1908,2113,2120,2124,2130,2143,2147,2150,2178,2181],[11,12,5],"h1",{"id":13},"fundamentos-de-probabilidad",[15,16,17,18,22,23,26],"p",{},"La probabilidad es una rama de las matemáticas que se ocupa de la verosimilitud de que ocurra un suceso. Es una forma de cuantificar la incertidumbre y medir la probabilidad de distintos resultados. En el contexto de los lanzamientos de moneda, la probabilidad se usa para determinar la verosimilitud de que la moneda caiga en ",[19,20,21],"strong",{},"cara"," o en ",[19,24,25],{},"cruz",".",[15,28,29],{},"Este artículo es una introducción al tema de la probabilidad. Nos quedaremos en lenguaje llano y usaremos una moneda como único ejemplo. Estadísticas más avanzadas llegarán en futuros artículos.",[31,32,34],"h2",{"id":33},"lo-básico","Lo básico",[15,36,37,38,177,178,181,182,185],{},"Cuando hablamos de probabilidad, estamos hablando de un concepto matemático que se puede representar de varias formas. La manera más común es como una fracción, un decimal o un porcentaje. Por ejemplo, si lanzas una moneda justa, la probabilidad de que caiga en cara es ",[39,40,43,72],"span",{"className":41},[42],"katex",[39,44,47],{"className":45},[46],"katex-mathml",[48,49,51],"math",{"xmlns":50},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[52,53,54,67],"semantics",{},[55,56,57],"mrow",{},[58,59,60,64],"mfrac",{},[61,62,63],"mn",{},"1",[61,65,66],{},"2",[68,69,71],"annotation",{"encoding":70},"application\u002Fx-tex","\\frac{1}{2}",[39,73,77],{"className":74,"ariaHidden":76},[75],"katex-html","true",[39,78,81,86],{"className":79},[80],"base",[39,82],{"className":83,"style":85},[84],"strut","height:1.1901em;vertical-align:-0.345em;",[39,87,90,95,173],{"className":88},[89],"mord",[39,91],{"className":92},[93,94],"mopen","nulldelimiter",[39,96,98],{"className":97},[58],[39,99,103,164],{"className":100},[101,102],"vlist-t","vlist-t2",[39,104,107,159],{"className":105},[106],"vlist-r",[39,108,112,133,144],{"className":109,"style":111},[110],"vlist","height:0.8451em;",[39,113,115,120],{"style":114},"top:-2.655em;",[39,116],{"className":117,"style":119},[118],"pstrut","height:3em;",[39,121,127],{"className":122},[123,124,125,126],"sizing","reset-size6","size3","mtight",[39,128,130],{"className":129},[89,126],[39,131,66],{"className":132},[89,126],[39,134,136,139],{"style":135},"top:-3.23em;",[39,137],{"className":138,"style":119},[118],[39,140],{"className":141,"style":143},[142],"frac-line","border-bottom-width:0.04em;",[39,145,147,150],{"style":146},"top:-3.394em;",[39,148],{"className":149,"style":119},[118],[39,151,153],{"className":152},[123,124,125,126],[39,154,156],{"className":155},[89,126],[39,157,63],{"className":158},[89,126],[39,160,163],{"className":161},[162],"vlist-s","​",[39,165,167],{"className":166},[106],[39,168,171],{"className":169,"style":170},[110],"height:0.345em;",[39,172],{},[39,174],{"className":175},[176,94],"mclose",", que es lo mismo que ",[19,179,180],{},"0,5"," o ",[19,183,184],{},"50%",". Las tres representaciones son equivalentes y se pueden usar indistintamente.",[15,187,188,189,196],{},"Como veremos en ",[190,191,195],"a",{"href":192,"rel":193},"https:\u002F\u002Fflipthecoin.app\u002Fes\u002Fblog\u002Fla-estadistica-inesperada-de-los-lanzamientos-de-moneda",[194],"nofollow","el artículo La estadística inesperada de los lanzamientos de moneda",", la probabilidad real de aterrizaje de una moneda no es exactamente 50-50 cada vez.",[31,198,200],{"id":199},"resultados-y-sucesos","Resultados y sucesos",[15,202,203],{},"Antes de seguir, dos piezas pequeñas de vocabulario:",[205,206,207,225],"ul",{},[208,209,210,211,214,215,218,219,221,222,26],"li",{},"Un ",[19,212,213],{},"resultado"," es una de las cosas posibles que pueden ocurrir. Cuando lanzas una moneda, los resultados son ",[216,217,21],"em",{},", ",[216,220,25],{}," y (muy raramente) ",[216,223,224],{},"canto",[208,226,210,227,230],{},[19,228,229],{},"suceso"," es una pregunta que hacemos sobre los resultados, como \"¿cayó en cara?\" o \"¿cayó en alguna cara?\".",[15,232,233],{},"La probabilidad es la herramienta que usamos para ponerle un número a lo probable que es un suceso.",[31,235,237],{"id":236},"la-escala-de-probabilidad","La escala de probabilidad",[15,239,240,241,244],{},"Las probabilidades siempre viven en una escala de ",[19,242,243],{},"0 a 1",":",[205,246,247,253,258],{},[208,248,249,252],{},[19,250,251],{},"0"," significa que el suceso es imposible. Una moneda convirtiéndose en paloma en pleno vuelo tiene probabilidad 0.",[208,254,255,257],{},[19,256,63],{}," significa que el suceso es seguro. Una moneda lanzada al aire acabando por caer, gracias a la gravedad, tiene probabilidad 1.",[208,259,260,261,26],{},"Cualquier cosa entre medias es \"algo probable\". Una moneda justa cayendo en cara se sitúa justo en el medio, en ",[19,262,180],{},[15,264,265,266,269,270,273],{},"En términos de porcentaje, esa misma escala va del ",[19,267,268],{},"0%"," al ",[19,271,272],{},"100%",". La misma idea, expresada de otra forma.",[31,275,277],{"id":276},"la-regla-del-complemento","La regla del complemento",[15,279,280,281,284,285,288],{},"Cada suceso tiene una imagen espejo llamada su ",[19,282,283],{},"complemento",": el suceso de que ",[216,286,287],{},"no"," ocurra. Y como algo o bien ocurre o bien no, las dos probabilidades siempre suman 1. En símbolos:",[15,290,293],{"className":291},[292],"math-block",[39,294,296,343],{"className":295},[42],[39,297,299],{"className":298},[46],[48,300,301],{"xmlns":50},[52,302,303,340],{},[55,304,305,309,314,318,321,324,327,329,332,334,336,338],{},[306,307,308],"mi",{},"P",[310,311,313],"mo",{"stretchy":312},"false","(",[315,316,317],"mtext",{},"no ",[306,319,320],{},"A",[310,322,323],{"stretchy":312},")",[310,325,326],{},"=",[61,328,63],{},[310,330,331],{},"−",[306,333,308],{},[310,335,313],{"stretchy":312},[306,337,320],{},[310,339,323],{"stretchy":312},[68,341,342],{"encoding":70},"P(\\text{no } A) = 1 - P(A)",[39,344,346,386,407],{"className":345,"ariaHidden":76},[75],[39,347,349,353,358,361,368,371,374,379,383],{"className":348},[80],[39,350],{"className":351,"style":352},[84],"height:1em;vertical-align:-0.25em;",[39,354,308],{"className":355,"style":357},[89,356],"mathnormal","margin-right:0.1389em;",[39,359,313],{"className":360},[93],[39,362,365],{"className":363},[89,364],"text",[39,366,317],{"className":367},[89],[39,369,320],{"className":370},[89,356],[39,372,323],{"className":373},[176],[39,375],{"className":376,"style":378},[377],"mspace","margin-right:0.2778em;",[39,380,326],{"className":381},[382],"mrel",[39,384],{"className":385,"style":378},[377],[39,387,389,393,396,400,404],{"className":388},[80],[39,390],{"className":391,"style":392},[84],"height:0.7278em;vertical-align:-0.0833em;",[39,394,63],{"className":395},[89],[39,397],{"className":398,"style":399},[377],"margin-right:0.2222em;",[39,401,331],{"className":402},[403],"mbin",[39,405],{"className":406,"style":399},[377],[39,408,410,413,416,419,422],{"className":409},[80],[39,411],{"className":412,"style":352},[84],[39,414,308],{"className":415,"style":357},[89,356],[39,417,313],{"className":418},[93],[39,420,320],{"className":421},[89,356],[39,423,323],{"className":424},[176],[15,426,427],{},"Para una moneda justa:",[205,429,430,660],{},[208,431,432,519,520,26],{},[39,433,435,465],{"className":434},[42],[39,436,438],{"className":437},[46],[48,439,440],{"xmlns":50},[52,441,442,462],{},[55,443,444,446,448,450,452,454,456,459],{},[306,445,308],{},[310,447,313],{"stretchy":312},[315,449,21],{},[310,451,323],{"stretchy":312},[310,453,326],{},[61,455,251],{},[310,457,458],{"separator":76},",",[61,460,461],{},"5",[68,463,464],{"encoding":70},"P(\\text{cara}) = 0,5",[39,466,468,498],{"className":467,"ariaHidden":76},[75],[39,469,471,474,477,480,486,489,492,495],{"className":470},[80],[39,472],{"className":473,"style":352},[84],[39,475,308],{"className":476,"style":357},[89,356],[39,478,313],{"className":479},[93],[39,481,483],{"className":482},[89,364],[39,484,21],{"className":485},[89],[39,487,323],{"className":488},[176],[39,490],{"className":491,"style":378},[377],[39,493,326],{"className":494},[382],[39,496],{"className":497,"style":378},[377],[39,499,501,505,508,512,516],{"className":500},[80],[39,502],{"className":503,"style":504},[84],"height:0.8389em;vertical-align:-0.1944em;",[39,506,251],{"className":507},[89],[39,509,458],{"className":510},[511],"mpunct",[39,513],{"className":514,"style":515},[377],"margin-right:0.1667em;",[39,517,461],{"className":518},[89],", así que ",[39,521,523,564],{"className":522},[42],[39,524,526],{"className":525},[46],[48,527,528],{"xmlns":50},[52,529,530,561],{},[55,531,532,534,536,539,541,543,545,547,549,551,553,555,557,559],{},[306,533,308],{},[310,535,313],{"stretchy":312},[315,537,538],{},"no cara",[310,540,323],{"stretchy":312},[310,542,326],{},[61,544,63],{},[310,546,331],{},[61,548,251],{},[310,550,458],{"separator":76},[61,552,461],{},[310,554,326],{},[61,556,251],{},[310,558,458],{"separator":76},[61,560,461],{},[68,562,563],{"encoding":70},"P(\\text{no cara}) = 1 - 0,5 = 0,5",[39,565,567,597,615,642],{"className":566,"ariaHidden":76},[75],[39,568,570,573,576,579,585,588,591,594],{"className":569},[80],[39,571],{"className":572,"style":352},[84],[39,574,308],{"className":575,"style":357},[89,356],[39,577,313],{"className":578},[93],[39,580,582],{"className":581},[89,364],[39,583,538],{"className":584},[89],[39,586,323],{"className":587},[176],[39,589],{"className":590,"style":378},[377],[39,592,326],{"className":593},[382],[39,595],{"className":596,"style":378},[377],[39,598,600,603,606,609,612],{"className":599},[80],[39,601],{"className":602,"style":392},[84],[39,604,63],{"className":605},[89],[39,607],{"className":608,"style":399},[377],[39,610,331],{"className":611},[403],[39,613],{"className":614,"style":399},[377],[39,616,618,621,624,627,630,633,636,639],{"className":617},[80],[39,619],{"className":620,"style":504},[84],[39,622,251],{"className":623},[89],[39,625,458],{"className":626},[511],[39,628],{"className":629,"style":515},[377],[39,631,461],{"className":632},[89],[39,634],{"className":635,"style":378},[377],[39,637,326],{"className":638},[382],[39,640],{"className":641,"style":378},[377],[39,643,645,648,651,654,657],{"className":644},[80],[39,646],{"className":647,"style":504},[84],[39,649,251],{"className":650},[89],[39,652,458],{"className":653},[511],[39,655],{"className":656,"style":515},[377],[39,658,461],{"className":659},[89],[208,661,662,864,865,869],{},[39,663,665,712],{"className":664},[42],[39,666,668],{"className":667},[46],[48,669,670],{"xmlns":50},[52,671,672,709],{},[55,673,674,676,678,681,683,686,688,690,700,702,704,706],{},[306,675,308],{},[310,677,313],{"stretchy":312},[315,679,680],{},"cara o cruz",[310,682,323],{"stretchy":312},[310,684,685],{},"≈",[61,687,63],{},[310,689,331],{},[691,692,693],"mstyle",{"scriptlevel":251,"displaystyle":312},[58,694,695,697],{},[61,696,63],{},[61,698,699],{},"6000",[310,701,685],{},[61,703,251],{},[310,705,458],{"separator":76},[61,707,708],{},"99983",[68,710,711],{"encoding":70},"P(\\text{cara o cruz}) \\approx 1 - \\tfrac{1}{6000} \\approx 0,99983",[39,713,715,745,763,846],{"className":714,"ariaHidden":76},[75],[39,716,718,721,724,727,733,736,739,742],{"className":717},[80],[39,719],{"className":720,"style":352},[84],[39,722,308],{"className":723,"style":357},[89,356],[39,725,313],{"className":726},[93],[39,728,730],{"className":729},[89,364],[39,731,680],{"className":732},[89],[39,734,323],{"className":735},[176],[39,737],{"className":738,"style":378},[377],[39,740,685],{"className":741},[382],[39,743],{"className":744,"style":378},[377],[39,746,748,751,754,757,760],{"className":747},[80],[39,749],{"className":750,"style":392},[84],[39,752,63],{"className":753},[89],[39,755],{"className":756,"style":399},[377],[39,758,331],{"className":759},[403],[39,761],{"className":762,"style":399},[377],[39,764,766,769,837,840,843],{"className":765},[80],[39,767],{"className":768,"style":85},[84],[39,770,772,775,834],{"className":771},[89],[39,773],{"className":774},[93,94],[39,776,778],{"className":777},[58],[39,779,781,826],{"className":780},[101,102],[39,782,784,823],{"className":783},[106],[39,785,787,801,809],{"className":786,"style":111},[110],[39,788,789,792],{"style":114},[39,790],{"className":791,"style":119},[118],[39,793,795],{"className":794},[123,124,125,126],[39,796,798],{"className":797},[89,126],[39,799,699],{"className":800},[89,126],[39,802,803,806],{"style":135},[39,804],{"className":805,"style":119},[118],[39,807],{"className":808,"style":143},[142],[39,810,811,814],{"style":146},[39,812],{"className":813,"style":119},[118],[39,815,817],{"className":816},[123,124,125,126],[39,818,820],{"className":819},[89,126],[39,821,63],{"className":822},[89,126],[39,824,163],{"className":825},[162],[39,827,829],{"className":828},[106],[39,830,832],{"className":831,"style":170},[110],[39,833],{},[39,835],{"className":836},[176,94],[39,838],{"className":839,"style":378},[377],[39,841,685],{"className":842},[382],[39,844],{"className":845,"style":378},[377],[39,847,849,852,855,858,861],{"className":848},[80],[39,850],{"className":851,"style":504},[84],[39,853,251],{"className":854},[89],[39,856,458],{"className":857},[511],[39,859],{"className":860,"style":515},[377],[39,862,708],{"className":863},[89],", porque la única otra opción es el raro \"canto\". (Más sobre ese 1 entre 6000 en ",[190,866,868],{"href":192,"rel":867},[194],"La estadística inesperada de los lanzamientos de moneda",".)",[15,871,872,873,876,877,880],{},"La regla del complemento suele ser la forma más fácil de calcular una probabilidad: en lugar de contar todas las formas en que algo ",[216,874,875],{},"puede"," pasar, cuenta la única forma en que ",[216,878,879],{},"no puede"," y réstala a 1.",[31,882,884],{"id":883},"combinar-sucesos-y-vs-o","Combinar sucesos: \"y\" vs \"o\"",[15,886,887],{},"La cosa se pone interesante cuando preguntamos por más de un lanzamiento a la vez. Dos reglas cubren casi todo lo que necesitarás:",[889,890,892],"h3",{"id":891},"y-ambas-cosas-ocurren","\"Y\" — ambas cosas ocurren",[15,894,895,896,899,900,903],{},"Los lanzamientos de moneda no se influyen entre sí (son ",[19,897,898],{},"independientes","). En este caso, ",[19,901,902],{},"multiplicas"," sus probabilidades:",[205,905,906,1064],{},[208,907,908,1063],{},[39,909,911,958],{"className":910},[42],[39,912,914],{"className":913},[46],[48,915,916],{"xmlns":50},[52,917,918,955],{},[55,919,920,922,924,927,929,931,933,935,937,940,942,944,946,948,950,952],{},[306,921,308],{},[310,923,313],{"stretchy":312},[315,925,926],{},"OO",[310,928,323],{"stretchy":312},[310,930,326],{},[61,932,251],{},[310,934,458],{"separator":76},[61,936,461],{},[310,938,939],{},"×",[61,941,251],{},[310,943,458],{"separator":76},[61,945,461],{},[310,947,326],{},[61,949,251],{},[310,951,458],{"separator":76},[61,953,954],{},"25",[68,956,957],{"encoding":70},"P(\\text{OO}) = 0,5 \\times 0,5 = 0,25",[39,959,961,991,1018,1045],{"className":960,"ariaHidden":76},[75],[39,962,964,967,970,973,979,982,985,988],{"className":963},[80],[39,965],{"className":966,"style":352},[84],[39,968,308],{"className":969,"style":357},[89,356],[39,971,313],{"className":972},[93],[39,974,976],{"className":975},[89,364],[39,977,926],{"className":978},[89],[39,980,323],{"className":981},[176],[39,983],{"className":984,"style":378},[377],[39,986,326],{"className":987},[382],[39,989],{"className":990,"style":378},[377],[39,992,994,997,1000,1003,1006,1009,1012,1015],{"className":993},[80],[39,995],{"className":996,"style":504},[84],[39,998,251],{"className":999},[89],[39,1001,458],{"className":1002},[511],[39,1004],{"className":1005,"style":515},[377],[39,1007,461],{"className":1008},[89],[39,1010],{"className":1011,"style":399},[377],[39,1013,939],{"className":1014},[403],[39,1016],{"className":1017,"style":399},[377],[39,1019,1021,1024,1027,1030,1033,1036,1039,1042],{"className":1020},[80],[39,1022],{"className":1023,"style":504},[84],[39,1025,251],{"className":1026},[89],[39,1028,458],{"className":1029},[511],[39,1031],{"className":1032,"style":515},[377],[39,1034,461],{"className":1035},[89],[39,1037],{"className":1038,"style":378},[377],[39,1040,326],{"className":1041},[382],[39,1043],{"className":1044,"style":378},[377],[39,1046,1048,1051,1054,1057,1060],{"className":1047},[80],[39,1049],{"className":1050,"style":504},[84],[39,1052,251],{"className":1053},[89],[39,1055,458],{"className":1056},[511],[39,1058],{"className":1059,"style":515},[377],[39,1061,954],{"className":1062},[89],", o 25%.",[208,1065,1066,1255],{},[39,1067,1069,1123],{"className":1068},[42],[39,1070,1072],{"className":1071},[46],[48,1073,1074],{"xmlns":50},[52,1075,1076,1120],{},[55,1077,1078,1080,1082,1085,1087,1089,1091,1093,1095,1097,1099,1101,1103,1105,1107,1109,1111,1113,1115,1117],{},[306,1079,308],{},[310,1081,313],{"stretchy":312},[315,1083,1084],{},"OOO",[310,1086,323],{"stretchy":312},[310,1088,326],{},[61,1090,251],{},[310,1092,458],{"separator":76},[61,1094,461],{},[310,1096,939],{},[61,1098,251],{},[310,1100,458],{"separator":76},[61,1102,461],{},[310,1104,939],{},[61,1106,251],{},[310,1108,458],{"separator":76},[61,1110,461],{},[310,1112,326],{},[61,1114,251],{},[310,1116,458],{"separator":76},[61,1118,1119],{},"125",[68,1121,1122],{"encoding":70},"P(\\text{OOO}) = 0,5 \\times 0,5 \\times 0,5 = 0,125",[39,1124,1126,1156,1183,1210,1237],{"className":1125,"ariaHidden":76},[75],[39,1127,1129,1132,1135,1138,1144,1147,1150,1153],{"className":1128},[80],[39,1130],{"className":1131,"style":352},[84],[39,1133,308],{"className":1134,"style":357},[89,356],[39,1136,313],{"className":1137},[93],[39,1139,1141],{"className":1140},[89,364],[39,1142,1084],{"className":1143},[89],[39,1145,323],{"className":1146},[176],[39,1148],{"className":1149,"style":378},[377],[39,1151,326],{"className":1152},[382],[39,1154],{"className":1155,"style":378},[377],[39,1157,1159,1162,1165,1168,1171,1174,1177,1180],{"className":1158},[80],[39,1160],{"className":1161,"style":504},[84],[39,1163,251],{"className":1164},[89],[39,1166,458],{"className":1167},[511],[39,1169],{"className":1170,"style":515},[377],[39,1172,461],{"className":1173},[89],[39,1175],{"className":1176,"style":399},[377],[39,1178,939],{"className":1179},[403],[39,1181],{"className":1182,"style":399},[377],[39,1184,1186,1189,1192,1195,1198,1201,1204,1207],{"className":1185},[80],[39,1187],{"className":1188,"style":504},[84],[39,1190,251],{"className":1191},[89],[39,1193,458],{"className":1194},[511],[39,1196],{"className":1197,"style":515},[377],[39,1199,461],{"className":1200},[89],[39,1202],{"className":1203,"style":399},[377],[39,1205,939],{"className":1206},[403],[39,1208],{"className":1209,"style":399},[377],[39,1211,1213,1216,1219,1222,1225,1228,1231,1234],{"className":1212},[80],[39,1214],{"className":1215,"style":504},[84],[39,1217,251],{"className":1218},[89],[39,1220,458],{"className":1221},[511],[39,1223],{"className":1224,"style":515},[377],[39,1226,461],{"className":1227},[89],[39,1229],{"className":1230,"style":378},[377],[39,1232,326],{"className":1233},[382],[39,1235],{"className":1236,"style":378},[377],[39,1238,1240,1243,1246,1249,1252],{"className":1239},[80],[39,1241],{"className":1242,"style":504},[84],[39,1244,251],{"className":1245},[89],[39,1247,458],{"className":1248},[511],[39,1250],{"className":1251,"style":515},[377],[39,1253,1119],{"className":1254},[89],", o 12,5%.",[15,1257,1258,1259,1359],{},"Cada lanzamiento extra reduce la probabilidad a la mitad. Por eso las rachas largas resultan sorprendentes — no porque la moneda esté \"tocada\" para el otro lado, sino porque cada nuevo lanzamiento añade otro ",[39,1260,1262,1282],{"className":1261},[42],[39,1263,1265],{"className":1264},[46],[48,1266,1267],{"xmlns":50},[52,1268,1269,1279],{},[55,1270,1271],{},[691,1272,1273],{"scriptlevel":251,"displaystyle":312},[58,1274,1275,1277],{},[61,1276,63],{},[61,1278,66],{},[68,1280,1281],{"encoding":70},"\\tfrac{1}{2}",[39,1283,1285],{"className":1284,"ariaHidden":76},[75],[39,1286,1288,1291],{"className":1287},[80],[39,1289],{"className":1290,"style":85},[84],[39,1292,1294,1297,1356],{"className":1293},[89],[39,1295],{"className":1296},[93,94],[39,1298,1300],{"className":1299},[58],[39,1301,1303,1348],{"className":1302},[101,102],[39,1304,1306,1345],{"className":1305},[106],[39,1307,1309,1323,1331],{"className":1308,"style":111},[110],[39,1310,1311,1314],{"style":114},[39,1312],{"className":1313,"style":119},[118],[39,1315,1317],{"className":1316},[123,124,125,126],[39,1318,1320],{"className":1319},[89,126],[39,1321,66],{"className":1322},[89,126],[39,1324,1325,1328],{"style":135},[39,1326],{"className":1327,"style":119},[118],[39,1329],{"className":1330,"style":143},[142],[39,1332,1333,1336],{"style":146},[39,1334],{"className":1335,"style":119},[118],[39,1337,1339],{"className":1338},[123,124,125,126],[39,1340,1342],{"className":1341},[89,126],[39,1343,63],{"className":1344},[89,126],[39,1346,163],{"className":1347},[162],[39,1349,1351],{"className":1350},[106],[39,1352,1354],{"className":1353,"style":170},[110],[39,1355],{},[39,1357],{"className":1358},[176,94]," al producto.",[889,1361,1363],{"id":1362},"o-al-menos-una-de-varias-cosas-ocurre","\"O\" — al menos una de varias cosas ocurre",[15,1365,1366,1367,1370,1371,1374,1375,903],{},"Si dos resultados ",[19,1368,1369],{},"no pueden ocurrir al mismo tiempo"," (son ",[19,1372,1373],{},"mutuamente excluyentes","), ",[19,1376,1377],{},"sumas",[205,1379,1380,1552],{},[208,1381,1382,1551],{},[39,1383,1385,1433],{"className":1384},[42],[39,1386,1388],{"className":1387},[46],[48,1389,1390],{"xmlns":50},[52,1391,1392,1430],{},[55,1393,1394,1396,1398,1401,1404,1407,1409,1411,1413,1415,1417,1420,1422,1424,1426,1428],{},[306,1395,308],{},[310,1397,313],{"stretchy":312},[315,1399,1400],{},"O",[310,1402,1403],{},"∪",[315,1405,1406],{},"X",[310,1408,323],{"stretchy":312},[310,1410,326],{},[61,1412,251],{},[310,1414,458],{"separator":76},[61,1416,461],{},[310,1418,1419],{},"+",[61,1421,251],{},[310,1423,458],{"separator":76},[61,1425,461],{},[310,1427,326],{},[61,1429,63],{},[68,1431,1432],{"encoding":70},"P(\\text{O} \\cup \\text{X}) = 0,5 + 0,5 = 1",[39,1434,1436,1463,1487,1514,1541],{"className":1435,"ariaHidden":76},[75],[39,1437,1439,1442,1445,1448,1454,1457,1460],{"className":1438},[80],[39,1440],{"className":1441,"style":352},[84],[39,1443,308],{"className":1444,"style":357},[89,356],[39,1446,313],{"className":1447},[93],[39,1449,1451],{"className":1450},[89,364],[39,1452,1400],{"className":1453},[89],[39,1455],{"className":1456,"style":399},[377],[39,1458,1403],{"className":1459},[403],[39,1461],{"className":1462,"style":399},[377],[39,1464,1466,1469,1475,1478,1481,1484],{"className":1465},[80],[39,1467],{"className":1468,"style":352},[84],[39,1470,1472],{"className":1471},[89,364],[39,1473,1406],{"className":1474},[89],[39,1476,323],{"className":1477},[176],[39,1479],{"className":1480,"style":378},[377],[39,1482,326],{"className":1483},[382],[39,1485],{"className":1486,"style":378},[377],[39,1488,1490,1493,1496,1499,1502,1505,1508,1511],{"className":1489},[80],[39,1491],{"className":1492,"style":504},[84],[39,1494,251],{"className":1495},[89],[39,1497,458],{"className":1498},[511],[39,1500],{"className":1501,"style":515},[377],[39,1503,461],{"className":1504},[89],[39,1506],{"className":1507,"style":399},[377],[39,1509,1419],{"className":1510},[403],[39,1512],{"className":1513,"style":399},[377],[39,1515,1517,1520,1523,1526,1529,1532,1535,1538],{"className":1516},[80],[39,1518],{"className":1519,"style":504},[84],[39,1521,251],{"className":1522},[89],[39,1524,458],{"className":1525},[511],[39,1527],{"className":1528,"style":515},[377],[39,1530,461],{"className":1531},[89],[39,1533],{"className":1534,"style":378},[377],[39,1536,326],{"className":1537},[382],[39,1539],{"className":1540,"style":378},[377],[39,1542,1544,1548],{"className":1543},[80],[39,1545],{"className":1546,"style":1547},[84],"height:0.6444em;",[39,1549,63],{"className":1550},[89],". Nada sorprendente — eso es cualquier resultado no-canto.",[208,1553,1554,1900],{},[39,1555,1557,1612],{"className":1556},[42],[39,1558,1560],{"className":1559},[46],[48,1561,1562],{"xmlns":50},[52,1563,1564,1609],{},[55,1565,1566,1568,1570,1572,1574,1576,1578,1580,1589,1591,1599,1601],{},[306,1567,308],{},[310,1569,313],{"stretchy":312},[61,1571,63],{},[310,1573,1403],{},[61,1575,66],{},[310,1577,323],{"stretchy":312},[310,1579,326],{},[691,1581,1582],{"scriptlevel":251,"displaystyle":312},[58,1583,1584,1586],{},[61,1585,63],{},[61,1587,1588],{},"6",[310,1590,1419],{},[691,1592,1593],{"scriptlevel":251,"displaystyle":312},[58,1594,1595,1597],{},[61,1596,63],{},[61,1598,1588],{},[310,1600,326],{},[691,1602,1603],{"scriptlevel":251,"displaystyle":312},[58,1604,1605,1607],{},[61,1606,66],{},[61,1608,1588],{},[68,1610,1611],{"encoding":70},"P(1 \\cup 2) = \\tfrac{1}{6} + \\tfrac{1}{6} = \\tfrac{2}{6}",[39,1613,1615,1639,1660,1743,1826],{"className":1614,"ariaHidden":76},[75],[39,1616,1618,1621,1624,1627,1630,1633,1636],{"className":1617},[80],[39,1619],{"className":1620,"style":352},[84],[39,1622,308],{"className":1623,"style":357},[89,356],[39,1625,313],{"className":1626},[93],[39,1628,63],{"className":1629},[89],[39,1631],{"className":1632,"style":399},[377],[39,1634,1403],{"className":1635},[403],[39,1637],{"className":1638,"style":399},[377],[39,1640,1642,1645,1648,1651,1654,1657],{"className":1641},[80],[39,1643],{"className":1644,"style":352},[84],[39,1646,66],{"className":1647},[89],[39,1649,323],{"className":1650},[176],[39,1652],{"className":1653,"style":378},[377],[39,1655,326],{"className":1656},[382],[39,1658],{"className":1659,"style":378},[377],[39,1661,1663,1666,1734,1737,1740],{"className":1662},[80],[39,1664],{"className":1665,"style":85},[84],[39,1667,1669,1672,1731],{"className":1668},[89],[39,1670],{"className":1671},[93,94],[39,1673,1675],{"className":1674},[58],[39,1676,1678,1723],{"className":1677},[101,102],[39,1679,1681,1720],{"className":1680},[106],[39,1682,1684,1698,1706],{"className":1683,"style":111},[110],[39,1685,1686,1689],{"style":114},[39,1687],{"className":1688,"style":119},[118],[39,1690,1692],{"className":1691},[123,124,125,126],[39,1693,1695],{"className":1694},[89,126],[39,1696,1588],{"className":1697},[89,126],[39,1699,1700,1703],{"style":135},[39,1701],{"className":1702,"style":119},[118],[39,1704],{"className":1705,"style":143},[142],[39,1707,1708,1711],{"style":146},[39,1709],{"className":1710,"style":119},[118],[39,1712,1714],{"className":1713},[123,124,125,126],[39,1715,1717],{"className":1716},[89,126],[39,1718,63],{"className":1719},[89,126],[39,1721,163],{"className":1722},[162],[39,1724,1726],{"className":1725},[106],[39,1727,1729],{"className":1728,"style":170},[110],[39,1730],{},[39,1732],{"className":1733},[176,94],[39,1735],{"className":1736,"style":399},[377],[39,1738,1419],{"className":1739},[403],[39,1741],{"className":1742,"style":399},[377],[39,1744,1746,1749,1817,1820,1823],{"className":1745},[80],[39,1747],{"className":1748,"style":85},[84],[39,1750,1752,1755,1814],{"className":1751},[89],[39,1753],{"className":1754},[93,94],[39,1756,1758],{"className":1757},[58],[39,1759,1761,1806],{"className":1760},[101,102],[39,1762,1764,1803],{"className":1763},[106],[39,1765,1767,1781,1789],{"className":1766,"style":111},[110],[39,1768,1769,1772],{"style":114},[39,1770],{"className":1771,"style":119},[118],[39,1773,1775],{"className":1774},[123,124,125,126],[39,1776,1778],{"className":1777},[89,126],[39,1779,1588],{"className":1780},[89,126],[39,1782,1783,1786],{"style":135},[39,1784],{"className":1785,"style":119},[118],[39,1787],{"className":1788,"style":143},[142],[39,1790,1791,1794],{"style":146},[39,1792],{"className":1793,"style":119},[118],[39,1795,1797],{"className":1796},[123,124,125,126],[39,1798,1800],{"className":1799},[89,126],[39,1801,63],{"className":1802},[89,126],[39,1804,163],{"className":1805},[162],[39,1807,1809],{"className":1808},[106],[39,1810,1812],{"className":1811,"style":170},[110],[39,1813],{},[39,1815],{"className":1816},[176,94],[39,1818],{"className":1819,"style":378},[377],[39,1821,326],{"className":1822},[382],[39,1824],{"className":1825,"style":378},[377],[39,1827,1829,1832],{"className":1828},[80],[39,1830],{"className":1831,"style":85},[84],[39,1833,1835,1838,1897],{"className":1834},[89],[39,1836],{"className":1837},[93,94],[39,1839,1841],{"className":1840},[58],[39,1842,1844,1889],{"className":1843},[101,102],[39,1845,1847,1886],{"className":1846},[106],[39,1848,1850,1864,1872],{"className":1849,"style":111},[110],[39,1851,1852,1855],{"style":114},[39,1853],{"className":1854,"style":119},[118],[39,1856,1858],{"className":1857},[123,124,125,126],[39,1859,1861],{"className":1860},[89,126],[39,1862,1588],{"className":1863},[89,126],[39,1865,1866,1869],{"style":135},[39,1867],{"className":1868,"style":119},[118],[39,1870],{"className":1871,"style":143},[142],[39,1873,1874,1877],{"style":146},[39,1875],{"className":1876,"style":119},[118],[39,1878,1880],{"className":1879},[123,124,125,126],[39,1881,1883],{"className":1882},[89,126],[39,1884,66],{"className":1885},[89,126],[39,1887,163],{"className":1888},[162],[39,1890,1892],{"className":1891},[106],[39,1893,1895],{"className":1894,"style":170},[110],[39,1896],{},[39,1898],{"className":1899},[176,94]," (sacar un 1 o un 2 en un dado de seis caras).",[15,1902,1903,1904,1907],{},"Si los sucesos ",[216,1905,1906],{},"pueden"," solaparse, la simple suma cuenta doble el solape y tienes que restarlo:",[15,1909,1911],{"className":1910},[292],[39,1912,1914,1974],{"className":1913},[42],[39,1915,1917],{"className":1916},[46],[48,1918,1919],{"xmlns":50},[52,1920,1921,1971],{},[55,1922,1923,1925,1927,1929,1931,1934,1936,1938,1940,1942,1944,1946,1948,1950,1952,1954,1956,1958,1960,1962,1964,1967,1969],{},[306,1924,308],{},[310,1926,313],{"stretchy":312},[306,1928,320],{},[310,1930,1403],{},[306,1932,1933],{},"B",[310,1935,323],{"stretchy":312},[310,1937,326],{},[306,1939,308],{},[310,1941,313],{"stretchy":312},[306,1943,320],{},[310,1945,323],{"stretchy":312},[310,1947,1419],{},[306,1949,308],{},[310,1951,313],{"stretchy":312},[306,1953,1933],{},[310,1955,323],{"stretchy":312},[310,1957,331],{},[306,1959,308],{},[310,1961,313],{"stretchy":312},[306,1963,320],{},[310,1965,1966],{},"∩",[306,1968,1933],{},[310,1970,323],{"stretchy":312},[68,1972,1973],{"encoding":70},"P(A \\cup B) = P(A) + P(B) - P(A \\cap B)",[39,1975,1977,2001,2023,2050,2077,2101],{"className":1976,"ariaHidden":76},[75],[39,1978,1980,1983,1986,1989,1992,1995,1998],{"className":1979},[80],[39,1981],{"className":1982,"style":352},[84],[39,1984,308],{"className":1985,"style":357},[89,356],[39,1987,313],{"className":1988},[93],[39,1990,320],{"className":1991},[89,356],[39,1993],{"className":1994,"style":399},[377],[39,1996,1403],{"className":1997},[403],[39,1999],{"className":2000,"style":399},[377],[39,2002,2004,2007,2011,2014,2017,2020],{"className":2003},[80],[39,2005],{"className":2006,"style":352},[84],[39,2008,1933],{"className":2009,"style":2010},[89,356],"margin-right:0.0502em;",[39,2012,323],{"className":2013},[176],[39,2015],{"className":2016,"style":378},[377],[39,2018,326],{"className":2019},[382],[39,2021],{"className":2022,"style":378},[377],[39,2024,2026,2029,2032,2035,2038,2041,2044,2047],{"className":2025},[80],[39,2027],{"className":2028,"style":352},[84],[39,2030,308],{"className":2031,"style":357},[89,356],[39,2033,313],{"className":2034},[93],[39,2036,320],{"className":2037},[89,356],[39,2039,323],{"className":2040},[176],[39,2042],{"className":2043,"style":399},[377],[39,2045,1419],{"className":2046},[403],[39,2048],{"className":2049,"style":399},[377],[39,2051,2053,2056,2059,2062,2065,2068,2071,2074],{"className":2052},[80],[39,2054],{"className":2055,"style":352},[84],[39,2057,308],{"className":2058,"style":357},[89,356],[39,2060,313],{"className":2061},[93],[39,2063,1933],{"className":2064,"style":2010},[89,356],[39,2066,323],{"className":2067},[176],[39,2069],{"className":2070,"style":399},[377],[39,2072,331],{"className":2073},[403],[39,2075],{"className":2076,"style":399},[377],[39,2078,2080,2083,2086,2089,2092,2095,2098],{"className":2079},[80],[39,2081],{"className":2082,"style":352},[84],[39,2084,308],{"className":2085,"style":357},[89,356],[39,2087,313],{"className":2088},[93],[39,2090,320],{"className":2091},[89,356],[39,2093],{"className":2094,"style":399},[377],[39,2096,1966],{"className":2097},[403],[39,2099],{"className":2100,"style":399},[377],[39,2102,2104,2107,2110],{"className":2103},[80],[39,2105],{"className":2106,"style":352},[84],[39,2108,1933],{"className":2109,"style":2010},[89,356],[39,2111,323],{"className":2112},[176],[15,2114,2115,2116,2119],{},"Eso es el ",[19,2117,2118],{},"principio de inclusión–exclusión",", y su versión más profunda es tema para un futuro artículo.",[31,2121,2123],{"id":2122},"una-nota-rápida-sobre-independencia","Una nota rápida sobre independencia",[15,2125,2126,2127,2129],{},"Dos sucesos son ",[19,2128,898],{}," cuando el resultado de uno no cambia la probabilidad del otro. Los lanzamientos de moneda son el ejemplo de libro: la moneda no tiene memoria, así que una racha de diez caras seguidas no hace que la cruz sea más probable en el undécimo lanzamiento.",[15,2131,2132,2133,2136,2137,2142],{},"Este es el montaje detrás de la famosa ",[19,2134,2135],{},"Falacia del jugador",", que desgrano en ",[190,2138,2141],{"href":2139,"rel":2140},"https:\u002F\u002Fflipthecoin.app\u002Fes\u002Fblog\u002Fla-estadistica-inesperada-de-los-lanzamientos-de-moneda#the-gamblers-fallacy",[194],"el artículo de estadísticas",". Por ahora, la versión corta: cada lanzamiento es un nuevo comienzo.",[31,2144,2146],{"id":2145},"conclusión","Conclusión",[15,2148,2149],{},"Eso es realmente todo para lo básico:",[2151,2152,2153,2156,2165,2175],"ol",{},[208,2154,2155],{},"Las probabilidades viven entre 0 y 1.",[208,2157,2158,2159,2161,2162,2164],{},"Usa el ",[19,2160,283],{}," (1 − P) cuando sea más fácil contar lo que ",[216,2163,287],{}," ocurre.",[208,2166,2167,2170,2171,2174],{},[19,2168,2169],{},"Multiplica"," para el \"y\", ",[19,2172,2173],{},"suma"," para el \"o\" mutuamente excluyente.",[208,2176,2177],{},"Los sucesos independientes no se preocupan por la historia del otro.",[15,2179,2180],{},"Con solo esas cuatro ideas puedes razonar sobre casi cualquier pregunta de lanzamiento de moneda — y sobre la mayoría de problemas tipo dados, cartas y lotería también.",[15,2182,2183,2184,2189],{},"Pon la teoría en práctica: ",[190,2185,2188],{"href":2186,"rel":2187},"https:\u002F\u002Fflipthecoin.app\u002Fes\u002Fplay",[194],"lanza una moneda online"," y sigue tu propia racha.",{"title":2191,"searchDepth":2192,"depth":2192,"links":2193},"",2,[2194,2195,2196,2197,2198,2203,2204],{"id":33,"depth":2192,"text":34},{"id":199,"depth":2192,"text":200},{"id":236,"depth":2192,"text":237},{"id":276,"depth":2192,"text":277},{"id":883,"depth":2192,"text":884,"children":2199},[2200,2202],{"id":891,"depth":2201,"text":892},3,{"id":1362,"depth":2201,"text":1363},{"id":2122,"depth":2192,"text":2123},{"id":2145,"depth":2192,"text":2146},"2026-04-23T01:00:00Z","Aprende los fundamentos de la probabilidad y cómo se relacionan con los lanzamientos de moneda.","md",{"excerpt":2209},{"type":8,"value":2210},[2211,2213,2219],[11,2212,5],{"id":13},[15,2214,17,2215,22,2217,26],{},[19,2216,21],{},[19,2218,25],{},[15,2220,29],{},true,"\u002Fblog\u002Fprobability-basics.es",{"title":5,"description":2206},"blog\u002Fprobability-basics.es","6yxNewZ-8-Ifp0r0_XaURHiahdISyPwS20XdYbgwuLY",{"en":2227,"es":13},"probability-basics",{"en":2227,"es":13},1779926070002]