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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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The correct Answer is:
`P(A) = 1//3; P(B) = 2//3; P(A nn B^(c )) = 1//12; P(A^(c )nn B) = 5//12`
`P(A^(c)) = 1 - P(A) or P(A) = 1 - P(A^(c)) = 1 - 2//3 = 1//3`
`P(A uu B) = P(A) + P(B) - P(A nn B)`
`implies 3//4 = 1//3 + P(B) - 1//4 implies P(B) = 2//3`
`P(A nn B^(c)) = P(A) - P(A nn B) = (1)/(3) - (1)/(4) = (1)/(12)`
`P(A^(c) nn B) = P(B) - P(A nn B) = (2)/(3) - (1)/(4) = (5)/(12)`
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