Question

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 probabilities of Atlanta winning each game are as follows: Game 1 2 3 4 5 6 7 Probability of Win 0.45 0.42 0.46 0.5 0.46 0.41 0.52 A.) What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places. B.) What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

Answer #1

**SOLUTION:**

From given data,

Game (X) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Probability of Win | 0.45 | 0.42 | 0.46 | 0.5 | 0.46 | 0.41 | 0.52 |

**A) What is the
probability that the Atlanta Braves win the World Series? If
required, round your answer to two decimal
places.**

P (That the Atlanta Braves win the World Series) = P(X = 2)

= 0.42

The probability that the Atlanta Braves win the World Series is 0.42

**B.) What is the
average number of games played regardless of winner? If required,
round your answer to one decimal place.**

E (X) = x p(x)

= (1* 0.45) + (2* 0.42) + (3* 0.46) + (4* 0.5) + (5* 0.46) + (6* 0.41) + (7* 0.52)

= 0.45+0.84+1.38+2+2.3+ 2.46 +3.64

= 13.07

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,...

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.

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?

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?

A team that wins 4 games out of 7 is the winner. Suppose that
Team S and Team R face each other in the final game and that Team S
has probability 0.55 of winning a single game over Team R .
Find:
The probability that Team S will win the series.

Consider a best-of-5 series, where a total of five games are
played, and whoever wins three or more games wins the series.
Suppose that you participate in such a series, and the probability
of you winning a game is 0.6. Assume that all games are played
independently.
(a) What is the probability that you win the series?
(b) What is the probability that the fifth game is necessary?
(i.e., 2-2 after game 4)
(c) Given that you had lost the...

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...

Markov Chains:
In baseball, basketball, tennis, and various other sports, the
winner of a tournament is determined by a best of five or best of
seven rule; that is, whichever team can win three or, respectively,
four games first is the winner of the series. Such tournaments are
presumed to be more fair than a single elimination game in
determining the better team, since the outcome of any single game
has a large element of chance. Suppose that two teams,...

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?

A team play a series of games with win, lose, or draw outcomes.
The transition probabilities between winning, losing, and drawing
are averaged over a long time and treated as independent: Loss Draw
Win Loss 0.3 0.4 0.3 Draw 0.4 0.5 0.1 Win 0.2 0.4 0.4 A. If the
team wins two games in a row, what is the probability that it will
draw its next game? B. On average the team wins 50% of the time,
draws 20% of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 10 minutes ago

asked 29 minutes ago

asked 33 minutes ago

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago