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.
