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If A and B are events such that P(A)...

If A and B are events such that `P(A)=(1)/(2), P(B) =(7)/(12) " and " P(A' uu B') =(1)/(4),` then A and B are

A

independent

B

mutually exclusive

C

both `a` and `b`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`P[(A nnB)'} =(1)/(4) rArr P(A nnB) =(1-(1)/(4)) =(3)/(4)`
Since `P(A nnB) ne 0 ` so A and B are not mutually exclusive
`P(A) xx P(B) =((1)/(2)xx (7)/(12))=(7)/(24) ne P(A nnB)`
`rArr ` A and B are not independet.
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