Question

5 girls are there. 4 are fair complexioned 2 are rich. If a be the event selecting a rich girl and b be the event selecting a fair complexioned girl. Find P(a/b).

Answer 1

2 - rich
3 - poor
These are independent events. Rich cannot be poor.

Probability of selecting a rich girl = 2/5 = A

Each of the 5 girls have equal chance to be fair complexioned. It is not dependent on whether they are rich or poor. Hence it is an independent event w.r.t to status ( rich/poor).

Probability of selecting a fair complexioned girl = 4/5 = B

Since those are independent events,
P( A intersection B ) = P(A) * P(B)

P(A/B) = P(A intersection B) / P(B)
= ( P(A) * P(B) ) / P(B)
= P(A)
= 2/5