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Question

Each of three identical jewellery boxes has two drawers. In each drawer of the first box, there is a gold watch. In each drawer of the second box, there is a silver watch. In one drawer of the third box, there is a gold watch while in the other, there is a silver watch. If we select a box at random, open one of the drawers and find it to contain a silver watch, then the probability that the other drawer has the gold watch in it, is

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Solution

The correct option is **A** 13

A: One box and one of its drawers randomly selected and a silver watch found in it

B1: It is the box C

B2: It is the box B

B3: It is the box A

P(B1)=P(B2)=P(B3)=13

P(A|B1)=12;P(A|B2)=1;P(A|B3)=0

P(B1|A)=P(A|B1)×P(B1)P(A|B1)×P(B1)+P(A|B2)×P(B2)+P(A|B3)×P(B3)

⇒P(B1|A)=1212+1=12⋅23=13

A: One box and one of its drawers randomly selected and a silver watch found in it

B1: It is the box C

B2: It is the box B

B3: It is the box A

P(B1)=P(B2)=P(B3)=13

P(A|B1)=12;P(A|B2)=1;P(A|B3)=0

P(B1|A)=P(A|B1)×P(B1)P(A|B1)×P(B1)+P(A|B2)×P(B2)+P(A|B3)×P(B3)

⇒P(B1|A)=1212+1=12⋅23=13

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