Question
Two schools, A and B participate in a Quiz competition.
The probability of A’s winning is 3/7 and the probability of B’s winning is 3/5. What is the probability that only one of them wins?Solution
Let A be the event of School A wins. Let B be the event of School B wins. Then A’ = Event of the School A fails and, B’ = Event of the School B fails Therefore P(A’) = 1 - 3/7 = 4/7 P(B’) = 1 - 3/5 = 2/5 Required Probability = P(A) × P(B’) + P(B) × P(A’) = 3/7 × 2/5 + 3/5 × 4/7 = 6/35 + 12/35 = 18/35
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