Probability (Mutually Exclusive and Independence)

Question

Events a, b, and c.

a and b are mutually exclusive.

a and c are independent.

P(a), P(b), P(aUc), P(bUc) are given.

How do I find P(c)?

Answer 1

If a and c are independent, P(AC) = P(A)P(C)

Then, as we are given P(A) and P(C), P(A U C) = P(A) + (C) - P(AC) = P(A) + P(C) - P(A)P(C) due to independence.