Question

If P(A) = `2/3`, P(B) = `2/5`, P(A ∪ B) = `1/3`, then find P(A ∩ B)

Answer 1

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`1/3 = 2/3 + 2/5 - "P"("A" ∩ "B")`

P(A ∩ B) = `2/3 + 2/5 - 1/3`

⇒ `(10 + 6 - 5)/15`

P(A ∩ B) = `11/15`