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Question

If A and B are independent events of a random experiment such that P(AB)=16 and P(¯¯¯¯A¯¯¯¯B)=13, then P(A) is equal to

A
13
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B
23
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C
57
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D
None of these
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Solution

The correct option is A 13
Given P(AB)=16 and P(¯¯¯¯A¯¯¯¯B)=13
P(¯¯¯¯A¯¯¯¯B)=P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=1P(AB)
P(AB)=113=23
We know that P(AB)=P(A)+P(B)P(AB)
P(A)+P(B)=23+16=56
Given A and B are independent events , so we get P(A)P(B)=P(AB)=16
By solving above equations , we get P(A)=13 and P(B)=12
Therefore option A is correct.

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