If the probability of picking a red ball out of bag A is 2/5 and the probability of picking a red ball out of bag B is 3/7, what is the chance that you will pick exactly 2 red balls if you pick 2 balls from A and 1 ball from B? The balls are not replaced.

Draw a tree diagram. Recognise that the second ball selected from bag A is dependent on the outcome of the first ball. The outcome of the ball selected from B is independent. There are 3 orders that 2 red balls can be take R R B, R B R or B R R. Find the probability of each route and then find the total probability by finding the sum of these values. 4/70 + 9/70 + 9/70 = 22/70