Consider a Stanley Cup playoff series in which the Toronto Maple Leafs hockey team faces the Ottawa Senators. Toronto hosts the first, second, and if needed, fifth and seventh games in this best-of-seven contest. The Leafs have a 65% chance of beating the Senators at home in he first game. After that, they have a 60%chance of a win at home if they won the previous game, but a 70% chance if they are bouncing back from a loss. Similarly, the Leaf's chances of victory in Ottawa are 40%after a win and 45% after a loss.

Question

Construct a tree diagram to illustrate all the possible outcomes of the first three games

A) consider the following events:
A={Leafs lose the first game but go on to win the series in the fifth game}
B={Leafs win the series n the fifth game}
C={Leafs lose the series in the fifth game}
Identify all the outcomes that make up each event, using strings of letters, such as LLSLL. Are any pairs from these three events mutually exclusive?

What is the probability of event A in part a)

What is the chance of the Leafs winning in exactly five games?

Explain how you found your answer to the previous questions?