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Formulas Utiles en Probabilidad

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formulas para un examen de estadistica

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Formulas Utiles en Probabilidad

  1. 1. FORMULAS ÚTILES EN PROBABILIDAD n! n n! nPr = ;   = nCr = r Técnicas de conteo: (n − r )!   (n − r )!r! P[ A] = n( A) # casos favorables a la ocurrencia de A = n( Ω) # casos posibles del experimento Probabilidad de la unión de eventos: P(A∪B)= P(A)+P(B) – P(A∩B) Si A y B son mutuamente excluyentes (disjuntos), entonces: P(A∪B)= P(A)+P(B) Probabilidad del evento contrario (complementario): P(A’)= 1 – P(A); P(A’|B)= 1 – P(A|B) P[ A ∩ B ] Probabilidad condicional: P[ A B] = P[ B ] intersección de eventos A y B cualquiera:  P[ A] × P[ B A] P[ A ∩ B] =   P[ B ] × P[ A B] Independencia ⇔ P[ A ∩ B ] = P[ A] × P[ B ] ; P[ A1 ∩ A2 ∩ ⋅ ⋅ ⋅ ∩ Ak ] = P[ A1 ] × P[ A2 ] × ⋅ ⋅ ⋅ × P[ Ak ] Probabilidad total: P[ B ] = P[ A'∩ B] + P[ A ∩ B] ; P[ A] = P[ A ∩ B] + P[ A ∩ B ' ] n En general P[ B ] = ∑ P[ B A ] ⋅ P[ A ] i =1 i i Regla de Bayes: P[ B A j ] ⋅ P[ A j ] P[ A j B] = n , para todo j: 1,2,3,...,n ∑ P[ B A ] ⋅ P[ A ] i =1 i i

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