Question

Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`

Answer 1

It is given that,

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

`\implies` P(A) = `5/26` and P(B) = `5/13`

`\implies` P(A | B) = `2/5`

`\implies (P(A ∩ B))/(P(B)) = 2/5`

`\implies P(A ∩ B) = 2/5 xx P(B)`

= `2/5 xx 5/13`

= `2/13`

It is known that,

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`\implies`  P(A ∪ B) = `5/26 + 5/13 - 2/13`

`\implies` P(A ∪ B) = `(5 + 10 - 4)/26`

`\implies` P(A ∪ B) = `11/26`