Question

Bag I contains 3 red and 4 black balls while another bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from bag II.

Answer 1

Let E₁ be the event of choosing the bag I, E₂ the event of choosing the bag II and A be the event of drawing a red ball.

Now, the probability of drawing a ball from bag II, being given that it is red, P(E₂/A). By using Bayes' theorem, we have