Question

What will be the value of P(A ∪ B) it 2P(A) = P(B) = `5/13` and P(A/B) = `?/5`

Options

• `5/13`

• `5/26`

• `11/26`

• `2/13`

Answer 1

`11/26`

Explanation:

We have 2P(A) = P(B) = `5/13`

P(A) = `5/26`, P(B) = `5/13`

P(A/B) = `(P(A ∩ B))/(P(B))` or `2/5 = (P(A ∩ B))/(5/13)`

P(A ∩ B) = `2/5 xx 5/13 = 2/13`

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `5/26 + 5/13 - 2/13`

= `(5 + 10 - 4)/26`

= `11/26`