A system can fail (event C) because of two possible causes (events A and B). The probabilities

Question:

A system can fail (event C) because of two possible causes (events A and B). The probabilities of A, B and A ∩ B are known, together with the probabilities of failure given A, given B and given A ∩ B. Express the following in terms of these known quantities:

(a) P(AUB) (c) P(CA U B) (b) P(CAN B)