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,