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.
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.