Two sacks, P P\,P and QQQ, contain gold, silver, and bronze discs. Sack P P\,P contains 5 gold discs, 2 silver discs, and 1 bronze disc. Sack Q Q\,Q contains 3 gold discs, 4 silver discs, and 5 bronze discs. Alex picks one disc at random from Sack P P\,P and places it into Sack QQQ. Alex then picks one disc at random from Sack QQQ.
Draw a tree diagram to represent this information.
Find the probability that Alex picks two discs of the same colour.
Given that both discs are the same colour, find the probability they are both gold.
198 exam-style questions on AQA A Level Maths 2.3 M: Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Conditional probability (A-level only), 2.3.3 Modelling with probability (A-level only), and 2.3 M: Probability. Each one has a worked solution and a mark scheme showing where the marks go.