Question

Suppose that the Toronto Blue Jays face the

New York Yankees in the division final. In
this best-of-five series, the winner is the first
team to win three games. The games are
played in Toronto and in New York, with
Toronto hosting the first, second, and if
needed, fifth games. The consensus among
experts is that Toronto has a 65% chance of
winning at home and a 40% chance of
winning in New York.

a) Construct a tree diagram to illustrate all
the possible outcomes.

b) What is the chance of Toronto winning
in three straight games?

Answer 1

I have attached my tree diagram. Pls. see attachment. Assuming that Toronto Blue Jays won the first 3 sets:

W W W = 65% * 65% * 40% = 16.90%

Other probabilities:
W W L = 65% * 65% * 60% = 25.35%
W L W = 65% * 35% * 40% = 9.10%
W L L = 65% * 35% * 60% = 13.65%
L W W = 35% * 65% * 40% = 9.10%
L W L = 35% * 65% * 60% = 13.65%
L L W = 35% * 35% * 40% = 4.90%
L L L = 35% * 35% * 60% = 7.35%

These probabilities are correct because when we all add up the probabilities, the sum is 100%