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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 (1) mutually exclusive and independent (2) equally likely but not independent (3) independent but not equally likely (4) independent and equally likely

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`P( bar (A uu B) = 1/6`
`1- P(A uu B) =1/6`
`P(A uu B) = 5/6`
`P(bar A) = 1/4`
`1- P(A) = 1/4`
`P(A) = 3/4`
`P(A uu B) = P(A) + P(B) - P(A nn B)`
`5/6 = 3/4 + P(B) - 1/4`
...
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