Quant Probability

There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?

Solution

Either bag A or bag B is selected. So, probability will be

P(selecting bag A) AND P(getting red ball) OR P(selecting bag B) AND P(getting red ball)

= P(A) × P(RA) + P(B) × P(RB)

= 1/2 × 4/9 + 1/2 × 5/11

= 2/9 + 5/22 = 89/198