A company has three machines that produce a component. Machine A produces 60% of the components. Machine B produces 25% of the components and machine C produces 15% of the components.
If a component is produced by machine A the chance that it will be faulty is 1%. 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 3%.
Draw a tree diagram to show this information.
A component is selected at random. Find the probability it is faulty.
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.