Question

If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.

पर्याय

• `3/4`

• `5/8`

• `5/4`

• `7/8`

Answer 1

If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to `underlinebb(5/8)`.

Explanation:

∵ P(A ∩ B) = P(A) + P(B) – P(A ∪ B)

= `1/3 + 1/5 - 1/2`

= `(10 + 6 - 15)/30`

= `1/30`

P(A ∩ B') = P(A) – P(A ∩ B)

= `1/3 - 1/30`

= `3/10`

P(B ∩ A') = P(B) – P(A ∩ B)

= `1/5 - 1/30`

= `1/6`

∴ P(A/B') + P(B/A') = `(P(A ∩ B^'))/(P(B^')) + (P(B ∩ A^'))/(P(A^'))`

= `3/10 xx 5/4 + 1/6 xx 3/2`

= `3/8 + 1/4`

= `5/8`