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If A and B are events such that P(A'uuB'...

If A and B are events such that `P(A'uuB') = (3)/(4), P(A'nnB') = (1)/(4)` and `P(A) = (1)/(3)`, then find the value of `P(A' nn B)`

Text Solution

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`P(A' uu B') = (3)/(4)`
`implies P((A nn B)') = (3)/(4)`
` implies P(A nn B) = (1)/(4)`
`P(A nn B) = (1)/(4)`
`implies P((A uu B)') = (1)/(4)`
`implies P(A uu B) = (3)/(4)`
Now, `P(A uu B) = P(A) + P(B) - P(A nn B)`
`implies (3)/(4) = (1)/(3) + P(B) - (1)/(4)`
`P(B) = (3)/(4) - (1)/(12) = (2)/(3)`
`therefore P(A' nn B)= P(B)-P(A nn B)`
`= (2)/(3) - (1)/(4) = (5)/(12)`
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