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Q.

Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box ,8. If a red ball is drawn from the selected box then the probability that it has come from box B is

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a

10/31

b

12/31

c

21/41

d

13/41

answer is B.

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Detailed Solution

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Let A1 be the event of selecting box A and A2 be the event of selecting box B. 

Then PA1=2PA2 and PA1+PA2=13PA2=1PA2=13,PA1=23

Let E be the event of drawing red ball from the selected bug.

PEA1=35,PEA2=47

PA2E=PA2PEA2PA1PEA1+PA2PEA2=13×4723×35+13×47=2042+20=2062=1031

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