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Let A and B be two events such that p( b...

Let A and B be two events such that `p( bar AuuB)=1/6, p(AnnB)=1/4` and `p( bar A)=1/4` , where ` bar A` stands for the complement of the event A. Then the events A and B are

A

mutually exclusive and independent

B

independent but not equally likely

C

equally likely but not independent

D

equally likely and mutually exclusive

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `P(bar(A uu B))=(1)/(6)` and `P(A nn B)=(1)/(4), P(bar(A))=(1)/(4)`
`P(A uu B)=1-P(bar(A uu B))=1-(1)/(6)=(5)/(6)`
and `P(A)=1-P(bar(A))=1-(1)/(4)=(3)/(4)`
`P(A uu B)=P(A)+P(B)-P(A nn B)`
`rArr (5)/(6)=(3)/(4)+P(B)-(1)/(4) rArr P(B) = (1)/(3)`
`rArr` A and B are not equally likely.
`P(A nn B) =P(A). P(B)=(1)/(4)`
So, events are independent.
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