In a ball hockey league, 16 teams make the playoffs. There are 4 rounds that team must
make it through to win the championship.
Round 1 is a best of 3 series
Rounds 2 and 3 are a best of 5 series
The championship round is a best of 7 series
You will be tracking the progress of the Dragons throughout their playoff journey. For
each problem:
Draw a tree diagram for how the series could play out
On your tree diagram, display the probabilities of the Dragons winning or losing (as decimals)
Show your calculations when computing probabilities of series outcomes (leave answers as decimals)
Summarize the Dragon’s chance of winning the series (as a percentage to 2 decimal places).
1) In the first round, they are playing the Unicorns. Since the
Dragons were the best team in the league, they play the first and
third game (if necessary) at home, where they have an 80%
chance of winning. They play the second game on the road,
where they have a 60% chance of winning.
Determine the probability that the Dragons win this best of three series.
2) In the second round, the Dragons are up against the Goldfish in
a best of five series. In this series the dragons have an 80%
chance of winning any game. Determine the probability that the
Dragons win this best of five series.
3) Things are getting intense in the third round. The Dragons are
up against the Pugs, and they have split the first two games (the
series is tied 1 – 1).
In this series momentum matters. After a win, the chance of winning increases by 10%. After a loss,
the chance of winning decreases by 10%. Initially, the Dragons have a 60% chance of winning the next
(third) game. Determine the probability that the Dragons win this best of five series. Note that there
are only three possible games left to be played. 4) In the championship round against the Manbearpigs, the Dragons got
off to a rough start losing two of the first three games. Things are getting
“super-serial”. Two more losses and the series is over.
The Dragons have a 50% chance of winning each of the remaining games.
Determine the probability that the Dragons come back and win this best of seven series.
Note that there are only four possible games left to be played, and that the Dragons lose the series if
they lose two more.
