Question

The World Series in baseball is won by the first team to win 4 games in a series of 7. Clearly it cannot go longer than 7 games. Assume the two teams are evenly matched. (a) What is the probability that the team to win the first game wins the series? Explain the reasoning behind your computation in words. (b) Suppose that a team wins the first two games. What is the chance that it wins the series?

Answer #1

The baseball World Series is won by the first team to win four
games. Suppose both teams are equally likely to win each game. What
is the probability that the team that wins the first game will win
the series?

In the baseball World Series, two teams play games until one
team has won four games; thus the total length of the series must
be between 4 and 7 games. What is the probability of having a World
Series with a length of 4 games under the assumption that the games
are independent events with each team equally likely to win?

11. A baseball team is known to win 75% of their games, and the
team wins 90% of their home games. 50% of the teamís games are at
home.
a. Given the team won their next game, what is the probability
that it was a home game?
b. Given the team lost their next game, what is the probability
it was a road game?

A volleyball team is entered in a tournament. Rounds of the
tournament are played as best of three; that is, each team will
play the opponent in that round until one of the teams has won two
games.
Suppose that teams are matched up evenly in the first round of
the tournament, such that either team has an equal chance to win.
For subsequent games, if a team had just won they will be more
confident and more likely to...

Two teams A and B play a series of at most five games. The first
team to win these games win the series. Assume that the outcomes of
the games are independent. Let p be the probability for team A to
win each game. Let x be the number of games needed for A to win.
Let the event Ak ={A wins on the kth trial}, k=3,4,5.
(a) What is P(A wins)?
Express the probability with p and k. Show...

In a baseball playoff series, the two teams are evenly matched.
The two teams must play until one team wins 4 games, and no ties
are possible. Use the rows of random numbers shown to approximate
the probability that the series will end in exactly 7 games

Baseball's World Series is a maximum of seven games, with the
winner being the first team to win four games. Assume that the
Atlanta Braves and the Minnesota Twins are playing in the World
Series and that the first two games are to be played in Atlanta,
the next three games at the Twins' ballpark, and the last two
games, if necessary, back in Atlanta. Taking into account the
projected starting pitchers for each game and the home field
advantage,...

The regular baseball season is 162 games. If a team wins 92
games, it will probably make the playoffs. If the team has a 50%
chance of winning each game, what is the probability that it will
win exactly 92 games? What is the probability that it will win at
least 92 games? Repeat these two calculations assuming the team to
have a 55% chance of winning each game. [You can make some
approximations if you like].

Suppose that two teams are playing a series of games, each team
independently wins each game with 1/2 probability. The final winner
of the series is the first team to win four games. Let X be the
number of games that the two teams have played. Find the
distribution of X.

Baseball's World Series is a maximum of seven games, with the
winner being the first team to win four games. Assume that the
Atlanta Braves and the Minnesota Twins are playing in the World
Series and that the first two games are to be played in Atlanta,
the next three games at the Twins' ballpark, and the last two
games, if necessary, back in Atlanta. Taking into account the
projected starting pitchers for each game and the home field
advantage,...

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