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.

Question

Philoid · Accepted Answer

Let us firstly assume, A₁ denote the events that a red ball is transferred from bag I to II

And, A₂ denote the event that a black ball is transferred from bag I to II

∴

And,

Let X 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,