Let S be the sample space and two mutually exclusive events A and B be such that A U B = S. If P(.) denotes the probability of the event. The maximum value of P(A)P(B) is ______ A. 0.5 B. 0.25 C. 0.125 D. 0.225 Answer Workspace Report Discuss Answer with explanation Answer: Option B Explanation 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 know 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, let’s 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. P(A).P(B) = 1 /4 = 0.25. Workspace

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