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. One counter is selected from bag A A\,A and placed in bag BBB, then one counter is selected from bag BBB.
Find the probability that the two selected counters have the same colour.
Given that they have the same colour, find the probability that both are yellow.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.