Question

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) = 2/3`, then P(B) is equal to ______. 

Options

• `1/2`

• `1/6`

• `1/3`

• `2/3`

Answer 1

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) = 2/3`, then P(B) is equal to `underlinebb(1/3)`. 

Explanation:

Given that, P(A) = `1/4, P(A/B) = 1/2`

and `P(B/A) = 2/3`

We know that,

`P(A/B) = (P(A ∩ B))/(P(B))`  ...(i)

and `P(B/A) = (P(B ∩ A))/(P(A))`  ...(ii)

∴ P(B) = `(P(B/A) . P(A))/(P(A/B))`

= `((2/3)(1/4))/((1/2))`

= `1/3`