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.
368 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.