Hi,

I just needed a bit of help with the following question.

Show that if A, B and C are mutually independent, then A and (B U C) are independent.

From what I understand if A, B and C are mutually independent then

P(AnBnC) = P(A)P(B)P(C)

P(AnB) = P(A)P(B)

P(AnC) = P(A)P(C)

P(BnC) = P(B)P(C)

To prove A and (B U C) are independent do I have to prove P(A|(BUC) ) = P(A) because I don't know what to do after

P((BUC)nA)/P(BUC) = P[(BnA)U(AnC)]/P(BUC)

THANK YOU