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!

Probability of the Union of Indepedent Events

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that if A1, A2, ..., An are independent events then
    P(A1 U A2 U ... An) = 1 - [1-P(A1)][1-P(A2)]...[1-P(An)]


    2. Relevant equations
    If A and B are independent then the probability of their intersection is P(A)P(B).
    The same can also be said of AC and B.

    3. The attempt at a solution
    I have managed to prove this algebraically for the case where n=2. But I am having trouble trying to do it for the general case since it is not as easy to break down the union of A1 through An into a union of disjoint sets as it was for n=2.
     
  2. jcsd
  3. Sep 12, 2009 #2
    Apply De Morgan's Law (for n events)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability of the Union of Indepedent Events
  1. Probability of events (Replies: 1)

  2. Probability unions (Replies: 2)

Loading...