Answer:
1. 27.46% probability that A wins the series in 3 games.
2. There is a 28.84% probability A wins the series in 4 games.
3. There is a 20.18% probability A wins the series in 5 games.
4. There is a 76.48% probability A wins the series.
5. There is a 71.825% probability A wins the series if a "best-of-three" game series is played.
Step-by-step explanation:
For each game, there are these following probabilities:
A 65% probability team A wins.
A 35% probability team B wins.
The combination formula is important to solve this problem:
This is because for example, team A winning games 1,2 and 4 and team B winning game 3 is the same as team A winning games 1,3,4 and team B winning game 2. That is, the order is not important.
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
1. What the probability that A wins the series in 3 games?
This is team A winning all 3 games. For each game, there is a 65% probability that team A wins. So
There is a 27.46% probability that A wins the series in 3 games.
2. What is the probability A wins the series in 4 games?
This is the team A winning three games and the team B 1. The team B win cannot happen in the fourth game, so the number of possibilities is a combination of 3 by 2. So
The probability that team A wins the series in 4 games is:
There is a 28.84% probability A wins the series in 4 games.
3.What is the probability A wins the series in 5 games?
This is the team A winning three games and the team B 2. The team B second win cannot happen in the fifth game, so the number of possibilities is a combination of 4 by 2. So
The probability that team A wins the series in 5 games is:
There is a 20.18% probability A wins the series in 5 games.
4. What is the probability A wins the series (period)?
They can win the series in 3,4 or 5 games. So this is the sum of the answers for 1,2,3.
So
There is a 76.48% probability A wins the series.
5. What is the probability A wins the series if a "best-of-three" game series is played?
These three following outcomes are accepted:
A - A
A - B - A
B - A - A
So
There is a 71.825% probability A wins the series if a "best-of-three" game series is played.