Fifty people are asked which of football FFF, golf G G\,G and hockey H H\,H they watch. Five watch all three; 8 watch football and golf; 7 watch golf and hockey; 9 watch football and hockey. The totals watching football, golf and hockey are 31, 13 and 17 respectively. Pairwise totals include those who watch all three.
Find the number who watch football but not hockey.
Given that a person watches football, find the probability that they do not watch hockey.
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.