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Question

If A and B are events such that P(¯¯¯¯A¯¯¯¯B)=34,P(¯¯¯¯A¯¯¯¯B)=14 and P(A)=13, then P(¯¯¯¯AB) is

A
512
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B
38
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C
58
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D
14
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Solution

The correct option is A 512

P(¯¯¯¯A¯¯¯¯B)=34P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=34P(AB)=14

P(¯¯¯¯A¯¯¯¯B)=14P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=14P(AB)=34

P(A)=13,P(¯¯¯¯A)=23

P(¯¯¯¯AB)=P(B)P(AB)

P(AB)=P(A)+P(B)P(AB)

34=13+P(B)14

P(B)=34112=9112=812=23

P(¯¯¯¯AB)=2314=8312=512


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