If A and B are two enents such that `P (A uuB)=3/4, P(A nnB)=1/4, P(barA)=2/3,` then `P(barA nnB)` is equal to

Options

A. `5/12`
B. `3/8`
C. `5/8`
D. `1/2`

Answer

A

Explanation

`P ( A) = 1 - P ( barA ) = 1 - ( 2 ) /( 3 ) = ( 1 ) /( 3 ) `
Using , ` P(A uuB ) = P(A) + P ( B) - P ( A nnB ) `
` rArr ( 3 ) /( 4 ) = ( 1 )/( 3 ) + P ( B) - ( 1 )/(4 ) rArr P ( B) = ( 2 ) /( 3 ) `
Now, ` P ( bar A nnB ) = P ( B) - P (A nnB ) `
` = (2 ) / ( 3) - ( 1 )/( 4 ) = (5 ) /( 12 ) `