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 (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.