Question

If A and B are such that P(A' ∪ B') = `2/3` and P(A ∪ B) = `5/9` then P(A') + P(B') = ______.

Answer 1

If A and B are such that P(A' ∪ B') = `2/3` and P(A ∪ B) = `5/9` then P(A') + P(B') = `10/9`.

Explanation:

Here P(A' ∪ B') = `2/3` and P(A ∪ B) = `5/9`

∴ 1 – P(A ∩ B) = `2/3`

⇒ P(A ∩ B) = `1 - 2/3 = 1/3`

Now P(A') + P(B') = 1 – P(A) + 1 – P(B)

= 2 – [P(A) + P(B)]

= 2 – [P(A ∪ B) + P(A ∩ B)]

= `2 - [5/9 + 1/3]`

= `2 - 8/9`

= `10/9`