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Question

A box ′A′ contains 2 white, 3 red and 2 black balls. Another box ′B′ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ′B′ is :

A
916
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B
716
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C
932
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D
78
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Solution

The correct option is B 716
P(E): Probability of choosing 1 red ball and 1 white ball.
P(Box A): Probability of choosing box A.
P(Box B): Probability of choosing box B.
Hence the required probabiity will be,
P(Box BE)=P(Box B)×P(EBox B)P(Box A)×P(EBox A)+P(Box B)×P(EBox B)P(Box BE)=12× 4C1× 2C1 9C212× 2C1× 3C1 7C2+12× 4C1× 2C1 9C2P(Box BE)=1917+19P(Box BE)=716

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