A certain sports team is the favourite to win the championship at the beginning of the season. They have been favoured to win the championship with a 55% chance at the start of the season. However, they have actually only won the championship 25% of the time they were favoured to win. When they have not been favoured to win at the start of the season, they have won the championship 10% of the time.

a. Construct a probability tree for this situation and use it to solve the following questions.

Season

Favored

%

Not Favored

%

Won the Championship

%

Did not win the Championship

%

Won the Championship

%

Did not win the Championship

%

b. If a season in the league's history is randomly selected, what is the probability that the team was the favourite at the start of the season and actually won the championship?

Round to 3 decimal places

c. What is the probability that, in a randomly selected season, the team won the championship and had not been the favourite?

Round to 3 decimal places

d. Given that the team won the championship in a particular season, what is the probability that they were not the favourite at the start of that season?