The probabilities of four cricketers A, B, C and D scoring more than $$50$$ runs in a match are $$12$$,$$13$$,$$14$$ $$and110$$ . It is known that exactly two of the players scored more than $$50$$ runs in a particular match. The probability that these players were A and B is

Question

The probabilities of four cricketers A, B, C and D scoring more than $$50$$  runs in a match are $$12$$,$$13$$,$$14$$     $$and110$$     . It is known that exactly two of the players scored more  than $$50$$ runs in a particular match. The probability that these players were A  and B is

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Let $$E1$$     be the event that exactly two players scored more than $$50$$  runs then $$P(E1)=12$$×$$13$$×$$34$$×$$910$$     $$+12$$×$$23$$×$$14$$×$$910+12$$×$$23$$×$$34$$×$$110+12$$×$$13$$×$$14$$×$$910$$     $$+12$$×$$23$$×$$34$$×$$110+12$$×$$23$$×$$14$$×$$110=65240$$       Let $$E2$$     be the event A and B scored more than $$50$$ runs, then $$P(E1$$∩$$E2)=12$$×$$13$$×$$34$$×$$910=27240$$     ∴     desired probability $$=$$ $$P(E2/E1)=P(E1$$∩$$E2)P(E1)=2765$$

The probabilities of four cricketers A, B, C and D scoring more than 50 runs in a match are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{10}$ . It is known that exactly two of the players scored more than 50 runs in a particular match. The probability that these players were A and B is

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The probabilities of four cricketers A, B, C and D scoring more than 50 runs in a match are 12,13,14 and110 . It is known that exactly two of the players scored more than 50 runs in a particular match. The probability that these players were A and B is

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The probabilities of four cricketers A, B, C and D scoring more than 50 runs in a match are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{10}$ . It is known that exactly two of the players scored more than 50 runs in a particular match. The probability that these players were A and B is