Two bags, A A\,A and BBB, contain red, green and yellow counters. Bag A A\,A contains 3 red counters, 2 green counters and 4 yellow counters. Bag B B\,B contains 5 red counters, 4 green counters and 1 yellow counter. Taylor picks one counter at random from bag A A\,A and places it into bag BBB. She then picks one counter at random from bag BBB.
Draw a tree diagram to represent this information.
Find the probability that Taylor picks two counters of the same colour.
Given that both counters are the same colour, find the probability they are both yellow.
