Question

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. Two balls are transferred at random 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 balls were  both black.

Answer 1

Let the events are defined as :

E₁ : 2 red balls are transferred from bag I to bag ll

E₂ : 2 black balls are transferred

E₃ : 1 red and 1 black ball is transferred

A  : 1 red ball is drawn from bag II

By Bayes' Theorem, the required probability is given by :