A coin is selected at random. Coin A A\,A is selected with probability 0.4 and has probability 0.7 of landing heads. Coin B B\,B is selected with probability 0.6 and has probability 0.3 of landing heads. The selected coin is tossed twice.
Find the probability of obtaining two heads.
Given that two heads are obtained, find the probability that coin A A\,A was selected.
Given that exactly one head is obtained, find the probability that coin A A\,A was selected.
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.