Question

# A box â€²Aâ€² contains 2 white, 3 red and 2 black balls. Another box â€²Bâ€² 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 â€²Bâ€² is

A
716
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B
932
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C
78
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D
916
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Solution

## The correct option is C 716For the bag A we can see that there are 2 white, 3 red and 2 black balls. Similarly, from bag B we have 4 white, 2 red and 3 black balls.Probability of choosing a white and then a red ball from bag B is given by =4C1× 2C19C2Probability of choosing a white ball then a red ball from bag A is given by =2C1× 3C17C2So, the probability of getting a white ball and then a red ball from bag B is given by 4C1× 2C19C24C1×2C19C2+2C1× 3C17C2 =2927+29=2×718+14=716

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