Suppose that A, B and C are independent events and P(C) ≠ 0. Prove:

a) P (A ∩ B | C) = P(A | C) P(B | C)

b) P (A ∪ B | C) = P(A | C) + P(B | C) - P (A ∩ B | C)

My book only this formula to proved the above question.

p(A | B) =(A ∩ B)/ P(B)

I dont know how to deal with 3 constants?

Any help?

Thanks