Yuliya is training for a triathlon. She is confident with her cycling, so is concentrating on running and swimming while training. It turns out that: • on 55% of the days she goes running • of the d

Yuliya is training for a triathlon. She is confident with her cycling, so is concentrating on running and swimming while training. It turns out that:

• on 55% of the days she goes running

• of the days that she goes running, on 60% of these days she also goes swimming.

(a) Let R denote the event Yuliya goes running while training, and let S denote the event that Yuliya goes swimming. Write the information given in the two bullet points in symbolic form.

(b) Calculate the probability that on a randomly chosen day Yuliya chooses to go running and swimming while training.

(c) Additional information is now given that Yuliya goes swimming on 50% of the days. Calculate the probability that on a randomly chosen day, while training, when Yuliya has chosen to go swimming that she also goes running.

(d) What is the probability that Yuliya chooses to run or swim, or both while training?

(e) For Yuliya, while training, are the events of running and swimming independent? Give a reason for your answer.