5. A keep-fit enthusiast swims, runs or cycles each day with probabilities \(0.2,0.3\) and 0.5 respectively. If he swims he then spends time in the sauna with probability 0.35 . The probabilities that he spends time in the sauna after running or cycling are 0.2 and 0.45 respectively.

1. Represent this information on a tree diagram.
2. Find the probability that on any particular day he uses the sauna.
3. Given that he uses the sauna one day, find the probability that he had been swimming.
4. Given that he did not use the sauna one day, find the probability that he had been swimming.