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Question

There are two bags, one of which contains 5 black and 4 white balls while the other contains 3 black and 6 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the first bag. But if it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a white ball.

A
12
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B
1427
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C
427
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D
1627
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Solution

The correct option is D 1627
Let E denotes the event of selecting white ball.
Let A denotes that the outcome on the die is either 1 or 3
and B denotes the outcome other than 1 and 3.
Then,
P(A) = 26 = 13P(B) = 46 = 23P(E|A) = 49P(E|B) = 69P(E)= P(E|A) P(A) + P(E|B) P(B)P(E) = 49×13 + 69×23P(E) = 1627

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