Question
There are two bags I and II. Bag I contains 3 white and 2 red balls and Bag II contains 5 white and 4 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.
Solution
Bag I, Bag II
Number of white balls = 3, Number of white balls = 5
Number of red balls = 2, Number of red balls = 4
Total number of balls = 5, Total number of balls = 9
Let E1 and E2 be the events of the ball being drawn from bag I and bag II respectively and E be the event that the drawn ball is red.
Since both the bags are equally likely to be selected
P(the red ball is drawn from bag II) = 
