Sample Space(S) - A set of all possible outcomes/events of a random experiment. Mutually Exclusive Events - Those events which can't occur simultaneously. P(A)+P(B)+P(A∩B)=1 Since the events are mutually exclusive, P(A∩B)=0. Therefore, P(A)+P(B)=1 Now, we now that AM >= GM So, (P(A)+P(B))/2 >= sqrt(P(A)*P(B)) P(A)*P(B) <= 1/4
Hence max(P(A)*P(B)) = 1/4.
We can think of this problem as flipping a coin, it has two mutually exclusive events ( head and tail , as both can't occur simultaneously). And sample space S = { head, tail } Now, lets say event A and B are getting a "head" and "tail" respectively. Hence, S = A U B. Therefore, P(A) = 1/2 and P(B) = 1/2. And, P(A).P(B) = 1 /4 = 0.25. Hence option B is the correct choice.