Question

If P(X ∩ Y) = `1/3` and P(X' ∩ Y') = `1/2`, P(X) = 2a and P(Y) = a, then the value of a is ______ 

Options

• `5/18`

• `1/3`

• `4/9`

• `1/9`

Answer 1

If P(X ∩ Y) = `1/3` and P(X' ∩ Y') = `1/2`, P(X) = 2a and P(Y) = a, then the value of a is `underline(5/18)`.

Explanation:

P(X' ∩ Y') = `1/2`

⇒ P[(X ∪ Y)'] = `1/2`

∴ 1 - P(X ∪ Y) = `1/2`

⇒ P(X ∪ Y) = `1 - 1/2 = 1/2`

∴ P(X) + P(Y) - P(X ∩ Y) = `1/2`

∴ 2a + a - `1/3 = 1/2`

⇒ `3a = 1/3 + 1/2 = 5/6 ⇒ a = 5/18`