If A and B are any two events such that `P(A uu B) = 3/4,`
`P(A nn B) = 1/4 and P(bar(A)) = 2/3`, where `bar(A)` stands for the complementary event of A, then what is P(B) ?

Options

A. `1/3`
B. `2/3`
C. `1/9`
D. `2/9`

Answer

B

Explanation

As given, `P(A uu B) = 3/4, P(A nn B) = 1/4`
and `P(bar(A)) = 2/3`
`P(bar(A)) = 1 - P(A) = 2/3 rArr P(A) = 1/3`
We know that
`P(A uu B) = P(A) + P(B) - P(A nn B)`
`rArr 3/4 = 1/3 + P(B) - 1/4`
`rArr 1 - 1/3 = P(B) rArr 2/3 = P(B)`