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 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.

Answer 1

Let E₁ and E₂ respectively denote the events that a red ball is transferred from bag I to II and a black ball is transferred from bag I to II.

Let A be the event that the ball drawn is red. 

When a red ball is transferred from bag I to II,