World Series, probability of victor with evenly matched teams

In summary, the probability of the World Series ending in only four games when two evenly matched teams meet is (1/2)^4. The probability of team A winning games 1, 2, 4, and 7 and team B winning games 3, 5, and 6 is (1/2)^7. The probability of team A winning the World Series in seven games when evenly matched is (1/2)^4. To find the probability of team A winning in either four or five games when the probability of A winning any given game is 1/4, the binomial distribution must be used.
  • #1
mamma_mia66
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Homework Statement



When two teams meet in the World Series, they play a series of games which stops when one team has won four games (a "best-of -seven" series). The team in the World Series are A and B.
(a) If the two teams are evently matched, what is the probability that the World Series ends in only four games?

(b) Again assuming they are equally matched, what is the probability that team A wins games 1,2,4 and 7 (and thus the World Series) and the team B wins games 3, 5 and 6?

(c) Again assuming they are equally matched, what is the probability that A wins the World Series in seven games?

(d) if the probability that A wins any given game against B is 1/4, what is the probability that A wins the World Series in either four of five games?



Homework Equations





The Attempt at a Solution



Ans for a) (1/2)^4

I don't know how to solve the problem after a). Please help. Thank you.
 
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  • #2


I think that its like this:

a) P(X = 0) + P(X = 4), X ~ Binomial(4, .5)
b) This is an ordered sequence, so since p = .5 then it is just .5^7
c) P(X = 4), X ~ Binomial(7, .5)
d) your question is incomplete. However, if the probability that A wins is p, then it is (P(X = 4), (X ~ Bin(4, p))) + (P(X = 4), (X ~ Bin(5, p))
 
  • #3


I don't think that I completely understand your answer, but Thank you.
 
  • #4


Look up the binomial distribution on wikipedia. You need to use its probability function to calculate the probabilities P(X = x).

the answers are:

<< answers deleted by berkeman -- giving answers to homework problems are not permitted on the PF >>
 
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  • #5


(c) and (d) are a bit more complicated than just the binomial distribution. For example, if we write "A" for a game that A wins and "B" for a game B wins, the binomial coefficient the number of different ways A could win four games and B one could be written AAAAB, AAABA, AABAA, ABAAA, and BAAAA- but the first of those is invalid in this problem because then the series would end in four games.
 
  • #6


it is not binomial distribution, it is like fliping coins:

a) is (1/2)^4 x (1/2)^4 for the two teams

b) is AABABBA which is 1,2, 4 and 7 win games for team A and 3,5 and 6 for team B
which is (1/2)^4 x (1/2)^3

c) is how many ways

d) I don't know yet, I am trying :confused:
 

FAQ: World Series, probability of victor with evenly matched teams

What is the World Series?

The World Series is the annual championship series of Major League Baseball (MLB). It is a best-of-seven playoff between the American League (AL) and National League (NL) champions.

How are the teams determined for the World Series?

The AL and NL champions are determined by winning their respective league's playoffs. The AL champion is the winner of the AL Championship Series and the NL champion is the winner of the NL Championship Series.

What is the probability of victory for evenly matched teams in the World Series?

The probability of victory for evenly matched teams in the World Series is approximately 50%. This means that each team has an equal chance of winning the series.

How is the home field advantage determined for the World Series?

The home field advantage in the World Series is determined by which team had the better regular season record. The team with the better record will have home field advantage for the first two games, and then the remaining games will be played at the other team's home stadium.

Has there ever been a tie in the World Series?

No, there has never been a tie in the World Series. In the event of a tie, additional games will be played until one team is declared the winner. However, there has not been a tie since 1922.

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