Question

If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.

Options

• `2/9`

• `7/9`

• `4/9`

• `5/9`

Answer 1

If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to `underlinebb(2/9)`.

Explanation:

Given,

`P(A/B) = 2 xx P(B/A)`

`\implies (P(A ∩ B))/(P(B)) = 2 xx (P(A ∩ B))/(P(A))`

`\implies` P(A) = 2P(B)  ...(i)

Now, P(A) + P(B) = `2/3`

From (i),

2P(B) + P(B) = `2/3`

`\implies` P(B) = `2/9`.