Question

Given there are two bags I and II. Bag I contains 3 red and 4 black bails while another bag II contains S 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 that the ball is drawn from the bag I and II and E₂ be the event that it is drawn from the bag II and E be the event that the drawn ball is red. 

Since the drawn ball is found to be red, so we have to Find P( E₂/A) the probability of drawing red ball from bag II. since both the bags are equally likely to be selected to draw the ball, we have

P(E₁) = P(E₂) = 1/2

Probability of getting red ball from bag I

= P(A/E₁) = 3/7

Probability of getting red ball from bag II

= P(A/E₂) = 5/11

Probability of getting red ball from bag III

= P(E₂/A)

Hence, using Baye’s Theorem,