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 and 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:

Let us first suppose that the events denoted by are the occurrences in which a red ball is transferred from bag I to bag II. In addition, denotes the occurrence in which a black ball is transported from bag I to bag II.

And,

Let be the event that the drawn ball is red when red ball is transferred from bag I to II,

And, when black ball is transferred from bag I to II,

Hence,