Of 60 students, 32 study music MMM, 28 study photography P P\,P and 24 study coding CCC. Fifteen study both music and photography, 12 study both photography and coding, 11 study both music and coding, and 6 study all three. Pairwise totals include those who study all three.
Find the number of students who study none of the three subjects.
Given that a student studies at least one of the subjects, find the probability that the student studies exactly one.
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.