2 Jimmy and Alan are playing a tennis match against each other. The winner of the match is the first player to win three sets. Jimmy won the first set and Alan won the second set. For each of the remaining sets, the probability that Jimmy wins a set is
- 0.7 if he won the previous set,
- 0.4 if Alan won the previous set.
It is not possible to draw a set.
- Draw a probability tree diagram to illustrate the possible outcomes for each of the remaining sets.
- Find the probability that Alan wins the match.
- Find the probability that the match ends after exactly four sets have been played.