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)
In the expression " A, B and C are independent events" how are you using independence?
EDIT
I see your reply to Ivy implies mutual independence.
Recall that if $\displaystyle A~\&~B$ are independent then so are $\displaystyle A^c~\&~B$.
It is simply a matter of set theory: $\displaystyle A\cup B\cup C=A\cup (A^c\cap B)\cup (A^c\cap B^c\cap C)$
That is all of $\displaystyle A$ with the part of $\displaystyle B$ left out with the part of $\displaystyle C$ left out of the second term.