Question
Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II, then a ball is drawn from bag II, the ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
Solution
Bag I contains 3 red and 4 black balls.
Bag II contain 4 red and 5 black balls.
Let E1 : Event that a red ball is drawn from bag I
E2 : Event that a black ball is drawn from bag I
After transferring a red ball from bag I to bag II, the bag II will have 5 red and 5 black balls.
Let A be the event of drawing red ball
Further when a black ball is transferred from bag I to bag II, it will contain 4 red and 6 black balls.
Required probability = 
