1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    AKG

    User Avatar
    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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A proof question involving union and complements of events
  1. Union proof (Replies: 2)

  2. Proof of union (Replies: 3)

Loading...