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Homework Help: A proof question involving union and complements of events

  1. Feb 27, 2008 #1
    1. The problem statement, all variables and given/known data
    If X1, X2, X3, ... Xk are independent events, prove that

    P(X1 U X2 U X3 U ... U Xk) = 1 - [1 - P(X1)][1-P(X2)]...[1-P(Xk)]

    2. Relevant equations
    3. The attempt at a solution
    Well I have tried a few methods, but I know it's got something to do with

    P(X1) = cc(P(X1)) (complment complement)
    P(X1) = 1 - c(P(X1))
    P(X1) = 1 - (1-P(X1))

    I know that much, but I can't link it in with unions of independent events?? I
  2. jcsd
  3. Feb 27, 2008 #2


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    Science Advisor
    Homework Helper

    DeMorgan's Law:

    [itex](A_1 \cup \dots \cup A_k)^c = A_1^c \cap \dots \cap A_k^c[/itex]
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