It is given that the events A and B are such that `P(A)=1/4, P(A/B)=1/2"and"p(B/A)=2/3dot` Then P(B) is: (1) `1/6` (2) `1/3` (3) `2/3` (4) `1/2`

Options

A. `(2)/(3)`
B. `(1)/(2)`
C. `(1)/(6)`
D. `(1)/(3)`

Answer

D

Explanation

We have,
`P(A cap B)=P(A)P(B//A)`
`therefore P(A cap B)=(1)/(4)xx(2)/(3)=(1)/(6)`
Now, `P(A//B)=(P(A cap B))/(P(B)) implies (1)/(2)=(1)/(6)xx(1)/(P(B)) implies P(B)=(1)/(3)`