This question was reported to be quite popular among the candidates and they performed well in it. Majority of the candidates were reported to correctly recall the relation P(AÈB) = P(A) + P(B) – P(AÇB). However, it was also observed that in part (a) some candidates multiplied the respective probabilities instead of adding them.
In part (a), since the events were mutually exclusive, P(A Ç B) = 0. Therefore, P(A È B) = P(A) + P(B) = + = .
In part (b), since the events were independent, then P(A Ç B) = P(A) × P(B) = × = . Therefore, P = P(A) + P(B) – P(A - .