A fair die is rolled. If the score is 1, 2, 3 or 4, bag A A\,A is selected; otherwise bag B B\,B is selected. Bag A A\,A contains 2 red and 3 blue counters. Bag B B\,B contains 4 red and 1 blue counter. A counter is drawn, replaced, and then a second counter is drawn from the selected bag.
Find the probability that both counters are red.
Given that both counters are red, find the probability that bag B B\,B was selected.
Determine whether the colours of the two counters are independent before the bag is known.
164 exam-style questions on OCR (MEI) A Level Maths 2.3.10 Conditional probabilities (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.