The probability that Sarah travels to her office by train, by bus, or by car is 35\frac{3}{5}53, 14\frac{1}{4}41, and 320\frac{3}{20}203 respectively. The probability of being late to work when using these methods of travel is 112\frac{1}{12}121, 15\frac{1}{5}51, and 13\frac{1}{3}31 respectively.
Draw a tree diagram to represent this information.
Find the probability that on a randomly chosen day: (i) Sarah travels by car and is late, (ii) Sarah is not late.
Given that Sarah is late, find the probability that she did not travel by train.
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.