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 4%. Given that a component is faulty, the probability it was produced by machine C is 531\displaystyle \frac{5}{31}315.
If a component is produced by machine C, find the probability that it will be faulty.
A component is selected at random. Find the probability it is faulty.
Draw a tree diagram to show this information.
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.