A quality control inspector examines precision components. The probability that a component is Grade A is 0.25 and the probability that it is Grade B is 0.75.
The inspector selects two components at random, one after the other. The first component is replaced before the second is selected.
Find the probability that the two components are of the same grade.
Find the probability that both components are Grade A, given that at least one of them is Grade A.
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.