Question

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?

Answer #1

This question follows binomial distribution with number of possible outcomes is 2 and the probability of each outcome, whether winning or losing is 0.5. The probability of having a World Series with a length of 4 games is =

There are only two cases when this is possible. Either the team 1 win the first 4 matches or the team 2 wins the first 4 matches. The probability of both the events happening is the same.

Now the probability of team 1 winning the first 4 matches = 4C4
* (0.5)^{4} * (0.5)^{0}

= 0.0625

The Probability of team 2 winning the first 4 matches will also be 0.0625

The required probability = 0.0625 + 0.0625 = 0.125

The baseball World Series is won by the first team to win four
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the series?

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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
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Two teams A and B play a series of games until one team wins
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a) 5 games
b) 6 games
c) 7 games
d) n games

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
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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...

Two teams play a series of games until one of the teams wins n
games. In every game, both teams have equal chances of winning and
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when (a) n = 2; (b) n = 3. (To keep track of what you are doing, it
can be easier to use different letters for the probabilities of win
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(a)
Find P(X = 5)
(b)
Find the expected number of games played.

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one of them has won 3 games. Suppose that each game played is,
independently, won by team A with probability
1/ 2 . Let X be the number of games that are
played.
(a)
Find P(X = 4)
(b)
Find the expected number of games played.

#5. Suppose that two teams (A and B) play a series of games that
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