Question

Find [P(B/A) + P(A/B)], if P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`.

Answer 1

Find `P(B/A) + P(A/B)`

Given, P(A) = `3/10`

P(B) = `2/5`

And P(A ∪ B) = `3/5`

Since, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`3/5 = 3/10 + 2/5 - P(A ∩ B)`

P(A ∩ B) = `7/10 - 3/5`

P(A ∩ B) = `1/10`

`P(B/A) + P(A/B) = (P(B ∩ A))/(P(A)) + (P(A ∩ B))/(P(B))`

= `(1/10)/(3/10) + (1/10)/(2/5)`

= `1/3 + 1/4`

= `7/12`