Question

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 first game of the series, what is the probability that your opponent wins the series?

(d) What is the probability that you win the series without winning any consecutive games?

Answer #1

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.

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
there are no draws. Compute the expected number of the games played
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
for the two teams).

Two teams A and B play a series of games until one team wins
four games. We assume that the games are played independently and
that the probability that A wins any game is p and B wins (1-p).
What is the probability that the series ends after...
a) 5 games
b) 6 games
c) 7 games
d) n games

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, are playing a best of 5 game series. (The
series is over once one team wins 3 games). The probability of A
winning any given game is 0.6. Draw the tree diagram for all
possible outcomes of the series.

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,...

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...

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 you are playing a series of ping pong games with Cl
́emonell until one of you has won six. Suppose that the probability
that Clemonemon wins is 0.58 and that the games are independent. 1.
What is the probability that the series ends at the ninth game? 2.
If the series ends at the ninth game, what is the probability that
you will win it

The probability that Cleveland wins a game over Golden State is
2/5 (0.4)
1 - What is the probability that
Golden State won the best of seven series over Cleveland in seven
games?
2 - What is the probability that
Cleveland won the series over Golden State in 6 games?
3 - What is the probability that
Golden State won the series over Cleveland in 5 games?
4 - What is the probability that Cleveland win the NBA
championship?

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