I am doing a basic probability problem from a textbook exercise. The question is as follows:
Consider two events A and B such that P(A) = 1/3 and P(B) = 1/2 and P(AB) = 1/8. Determine the value of P(BA^c). The way I did the problem is as, P(BA^c) = P(B(1-A)) --> step 1 = P(B - BA) --> step 2 = P(B) - P(BA) --> step 3 = (1/2) - (1/8) = 3/8.
Answer from the book is same as mine.Is my approach correct? Does the Probability holds the distributivity as I did it from step 2 to step 3?
Please correct me if I were wrong with my terminology.