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## Homework Statement

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)]

## Homework Equations

## 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