Question

There are 5 bags three of which each contains 5 white and 3 black balls, and remaining 2 bags each contains 2 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group.

Answer 1

Chances of selection of the first group is 3/5-----------------------------Chances of selection of second group is 2/5
Chances of selecting a black ball from group 1: 2/7----------------------Chances of selecting a black ball from group 2: 4/5

Thus combined probability of section of black ball from group 1:
3/5 x 2/7 = 6/35

Thus combined probability of section of black ball from group 2:
2/5 x 4/5 = 8/25

Out of these chances, chance of occurrence of first case : (6/35) / (6/35 + 8/25) = 15/43

This is a conditional probability