# Probability of the Union of Indepedent Events

1. Sep 12, 2009

### Obraz35

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. Sep 12, 2009

### VeeEight

Apply De Morgan's Law (for n events)