# Math Help - Proof

1. ## Proof

Using the general formula for P(A U B U C), prove the following:
If A, B and C are independent events, then
P(A) + P(A^c) * P(B) + P(A^c)*P(B^c)*P(C)

2. Originally Posted by cag31
Using the general formula for P(A U B U C), prove the following:
If A, B and C are independent events, then
P(A) + P(A^c) * P(B) + P(A^c)*P(B^c)*P(C)
Prove what? That's an expression- what do you want to prove about it?

3. Sorry, that P(A U B U C) = P(A) + P(A^C)*P(B)+P(A^c)*P(B^c)*P(C)

4. Originally Posted by cag31
If A, B and C are independent events
In the expression " A, B and C are independent events" how are you using independence?
EDIT
Recall that if $A~\&~B$ are independent then so are $A^c~\&~B$.
It is simply a matter of set theory: $A\cup B\cup C=A\cup (A^c\cap B)\cup (A^c\cap B^c\cap C)$
That is all of $A$ with the part of $B$ left out with the part of $C$ left out of the second term.