Respuesta :
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.
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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
[tex]P = (0.65)^{3} = 0.2746[/tex]
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
[tex]C_{3,2} = \frac{3!}{2!1!} = 3[/tex]
The probability that team A wins the series in 4 games is:
[tex]P = 3*(0.65)^{3}*(0.35) = 0.2884[/tex]
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
[tex]C_{4,2} = \frac{3!}{2!1!} = 6[/tex]
The probability that team A wins the series in 5 games is:
[tex]P = 6*(0.65)^{3}*(0.35)^{2} = 0.2018[/tex]
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
[tex]P = 0.2746 + 0.2884 + 0.2018 = 0.7648[/tex]
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
[tex]P = (0.65)^{2} + 2*(0.65)^{2}*(0.35) = 0.71825[/tex]
There is a 71.825% probability A wins the series if a "best-of-three" game series is played.
