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Question

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

A
521
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B
621
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C
1021
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D
1121
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Solution

The correct option is D 1121
Bag 1: {3 black , 4 white}
Bag 2: {4 black, 3 white }
Let E1 be the event bag 1 is selected and E2 be the event bag 2 is selected.
Let E be the event black ball is chosen
P(E1)=26,P(E2)=46
P(EE1)=37 and P(EE2)=47
Using Total Theorem of probablity,
P(E)=P(E1).P(E/E1)+P(E2).P(E/E2)
P(E)=26×37+46×47=2242=1121

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