Mathematics, 12.12.2019 20:31 zairaefh6496

In an nba championship series, the team that wins four games out of seven is the winner. suppose that teams and face each other in the championship games and that team has a probability 0.55 of winning a game over team b. a. what is the probability that team will win the series in 6 games? b. what is the probability that team will win the series? c. if teams and were facing each other in a regional playoff series, which is decided by winning three out of 5 games, what is the probability that team would win the series?

Answers: 3

Show answers

Answers

Answer from: whocares1234

a) P=0.185

b) P=0.608

c) P=0.593

Step-by-step explanation:

The question is not complete

"In an NBA championship series, the team that wins four games out of seven is the winner. Suppose that teams A and B face each other in the championship games and that team A has a probability 0.55 of winning a game over team B.

a. What is the probability that team A will win the series in 6 games?

b. What is the probability that team A will win the series?

c. If teams A and B were facing each other in a regional playoff series, which is decided by winning three out of 5 games, what is the probability that team A would win the series?

a) It is implicit that 6 games are played. The number of games needed to win a series in 6 games is 4, and the last winning should be in the 6th game.

So we have 5 random results in the first 5 games in which A team wins 3 matches and losses 2 matches.

This can be modeled as a binomial distribution with k=3, n=5 and p=0.55.

$P(k=3)=\frac{n!}{k!(n-k)!}p^k*(1-p)^{n-k}\\\\P(k=3)=\frac{5!}{3!2!}*0.55^3*0.45^2=10*0.166*0.203=0.337$

Then, this probability has to be multiplied by the probability of winning the last game.

$P(W_6)=P(k=3;n=5)*P(W_{6th})=0.337*0.55=0.185$

The probability that team A will win the series in 6 games is P=0.185.

b) In this case, we have to calculate the probability of A winning at least 4 games. When a team reaches 4 wins, the series is over. This can happen in 4, 5, 6 or 7 games.

The probability of winning the series is:

$P(W)=[P(3;3)+P(3;4)+P(3;5)+P(3;6)]*P(win\,last\,game)$

Probability of 3 wins in 3 games

$P(3;3)=\frac{3!}{3!0!}*0.55^3*0.45^0 =1*0.166*1=0.166$

Probability of 3 wins in 4 games

$P(3;4)=\frac{4!}{3!1!}*0.55^3*0.45^1 =4*0.166*0.45=0.299$

Probability of 3 wins in 5 games

$P(3;5)=\frac{5!}{3!2!}*0.55^3*0.45^2 =10*0.166*0.203=0.337$

Probability of 3 wins in 6 games

$P(3;6)=\frac{6!}{3!3!}*0.55^3*0.45^3 =20*0.166*0.091=0.303$

Then

$P(W)=[P(3;3)+P(3;4)+P(3;5)+P(3;6)]*P(win\,last\,game)\\\\P(W)=[0.166+0.299+0.337+0.303]*0.55=1.105*0.55=0.608$

The probability of team A of winning the series is P=0.608.

c) The probabilty of winning the regional playoff is

$P(W)=[P(2;2)+P(2;3)+P(2;4)]*P(win\,last\,game)$

$P(2;2)=\frac{2!}{2!0!}*0.55^2*0.45^0 =1*0.303*1=0.303\\\\P(2;3)=\frac{3!}{2!1!}*0.55^2*0.45^1 =3*0.303*0.45=0.408\\\\P(2;4)=\frac{4!}{2!2!}*0.55^2*0.45^2 =6*0.303*0.203=0.368$

Then,

$P(W)=[P(2;2)+P(2;3)+P(2;4)]*P(win\,last\,game)\\\\P(W)=[0.303+0.408+0.368]*0.55=1.079*0.55=0.593$

Answer from: Quest

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

Answer from: Quest

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

Another question on Mathematics

Mathematics, 21.06.2019 17:00

You are on a cycling trip around europe with friends. you check the weather forecast for the first week. these are the temperatures for the week. sun mon tues wed thurs fri sat 16°c 20°c 24°c 28°c 28°c 23°c 15°c what is the mean temperature forecast for the week?

Answers: 1

Answer

Mathematics, 21.06.2019 19:40

Which of the following three dimensional figures has a circle as it’s base

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

X/y + 4y/x divided by x/y - 2y/x explain as in depth as you can how you simplfied the fractions. i don't know where to start on this : /

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Acaterer charges $500 plus $30 per guest to cater a wedding. walt and traci don't want to spend more than $8000 on catering. write and solve an inequality in terms of the number of guests, g, that can be invited. a) 30g ? 8000; g ? 267 b) 500g < 8000; g < 16 c) 500 + 30g < 8000; g < 250 d) 500 + 30g ? 8000; g ? 250

Answers: 1

Answer

You know the right answer?

In an nba championship series, the team that wins four games out of seven is the winner. suppose tha...

Questions

Mathematics, 23.10.2020 06:01

Determine whether each equation represents a proportional relationship. If it does, identify the constant of proportionality. y = x + 1...