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Q.

Let Bfi=1,2,3 be three independent events in a sample space. The probability that only B1 occur is α,only  B2occurs is β and only B3occurs is γ. Let p be the probability that none of the eventsBf  occurs and these 4 probabilities satisfy the equations  α−2βp=αβand β−3γp=−2βγ (All the probabilities are assumed to lie in the interval (0, 1). Then  PB1PB3is equal to  _________.

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answer is 6.

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Detailed Solution

Let x, y, z be probability of B1, B2, B3 respectively⇒  x1−y1−z=α   ⇒y1−x1−z=β⇒  z1−x1−y=γ   ⇒1−x1−z=P Putting in the given relation we get x = 2y and y = 3z ⇒  x=6z  ⇒xz=6
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