A quality control inspector examines a batch of precision components. The probability that a component is 'Grade-A' (AAA) is 0.25, and the probability it is 'Grade-B' (BBB) is 0.75. The inspector selects two components at random, one after the other, with the first being replaced before the second is drawn.
Calculate the probability that both components are of the same grade.
Find the probability that both components are Grade-A, given that at least one of the components 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.