A company uses three machines, AAA, B B\,B and CCC, to produce a component.
Machine A A\,A produces 40% of the components, machine B B\,B produces 35% and machine C C\,C produces 25%.
Of the components produced by machine AAA, 3% are faulty. Of those produced by machine BBB, 2% are faulty. Of those produced by machine CCC, 1% are faulty.
A component is selected at random. Find the probability that it is faulty.
Given that the selected component is faulty, find the probability that it was produced by machine CCC.
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.