A city has three health clinics: Alpha, Beta, and Gamma. 45% of diagnostic tests are performed at Alpha, 30% at Beta, and 25% at Gamma.
At clinic Alpha, the probability of a false positive result is 2%. At clinic Beta, the probability of a false positive result is 3%. At clinic Gamma, the probability of a false positive result is 4%.
Draw a tree diagram to show this information.
A test result is selected at random. Find the probability it is a false positive.
Given that the test result is a false positive, find the probability it was performed at clinic Alpha.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.