A company has three machines that produce a component. Machine A produces 40% of the components. Machine B produces 35% of the components and machine C produces 25% of the components.
If a component is produced by machine A the chance that it will be faulty is 3%. If a component is produced by machine B the chance that it will be faulty is 2%. If a component is produced by machine C the chance that it will be faulty is 1%.
Draw a tree diagram to show this information.
A component is selected at random. Find the probability it is faulty, giving your answer in exact form.
Given that the component is faulty, find the probability it was produced by machine C.
330 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.