A jar contains 7 yellow marbles, 5 purple marbles, and 8 green marbles. Two marbles are selected at random from the jar without replacement.
Draw a tree diagram to represent this information.
Find the probability that both marbles selected are purple.
Given that at least one of the marbles selected is yellow, find the probability that both marbles are 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.