Two bags, A A\,A and BBB, contain red, green and yellow counters.
Bag A A\,A contains 3 red, 2 green and 4 yellow counters. Bag B B\,B contains 5 red, 4 green and 1 yellow counter.
Taylor takes one counter at random from bag A A\,A and places it into bag BBB. She then takes one counter at random from bag BBB.
Find the probability that Taylor's two counters are the same colour.
Given that the two counters are the same colour, find the probability that they are both yellow.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.