Suppose two teams are playing a series of games, each of which is independent. Team A...
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Suppose two teams are playing a series of games, each of which is independent. Team A has probability p of winning each game, and team B has probability 1 − p of winning each game. The winner of the series is the first team to win two games. Find the expected number of games played; note that this will be a function of p. [Hint: Let Xbe the total number of games played in the series and first determine the probability for each possible value of X.] Show that this expected number of games played is maximized when p = 1/2.
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Suppose two teams are playing a series of games, each of which
is independent. Team A...
Two teams are playing a series of soccer games, each of which is independent. Team 1...
Two teams are playing a series of soccer games, each of which is independent. Team 1 has probability p of winning each game, and team 2 has probability 1 − p of winning each game. The winner of the series is the first team to win two soccer games. Find the expected number of games played. This will be a function of p. Let Y be the total number of soccer games played in the series and first determine the...
Suppose that two teams are playing a series of games each of which is independently won by team A with probability p an...
Suppose that two teams are playing a series of games each of which is independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win i games. (a) If i 4, find the probability that a total of 7 games are played. (b) Find the expected number of games that are played when i 3.
Suppose that two teams are playing a series of games...
Problem 4. Two hockey teams, A and B play a series of games, until one of...
Problem 4. Two hockey teams, A and B play a series of games, until one of the teams wins 4 games. Suppose team A has probability p of winning each game, and games are independent. Let X be the total number of games that are played (a) Find the probability mass function of X (b) What is the probability that team A wins the series conditioned on X-47 (c) What is the probability that team A wins the series conditioned...
Two evenly matched baseball teams are playing a series of games in which the winner of...
Two evenly matched baseball teams are playing a series of games in which the winner of the series will be the first team to win 4 games. What is the probability that the series ends in exactly 6 games?
Problem 16-07 (Algorithmic) 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 are playing the Minnesota T...
Problem 16-07 (Algorithmic) 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 are playing the Minnesota Twins 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...
Teams A and Bare in a seven-game playoff series; the team that wins four games is...
Teams A and Bare in a seven-game playoff series; the team that wins four games is the team that wins the series. Assume that both teams are evenly matched (i.e., the probability of winning each game is 50/50). (1) Team A won the first two games. What is the probability that team B will win the series? (2) continue to assume that Team A has already won two games, but the teams are not evenly matched. Assume that B is...
Suppose that two teams play a series of games that ends when one of them has...
Suppose that two teams play a series of games that ends when one of them has won 3 games. Suppose that each game played is, independently, won by team A with probability Let X be the number of games that are played. (a) Find P(X = 4) (b) Find the expected number of games played.
Suppose that two teams, A and B play a series of games that ends when one...
Suppose that two teams, A and B play a series of games that ends when one of them has won 3 games. Suppose that games are played independently and both teams have equal chances of winning in each game. Let X be the number of games played. (i) Find the probability mass function of X. (ii) Find the expected value of X
X and Y play a series of games. X has a probability p of winning each...
X and Y play a series of games. X has a probability p of winning each game. To win the game, the player has to win 2 more games than the other first. (a) Find the probability that X is the overall winner. (b) Find the expected number of games played.
Problem 12-07 (Algorithmic) Baseball's World Series is a maximum of seven games, with the winner ...
Problem 12-07 (Algorithmic) 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...
Suppose that two teams are playing a series of games each of which is independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win i games. (a) If i 4, find the probability that a total of 7 games are played. (b) Find the expected number of games that are played when i 3.
Suppose that two teams are playing a series of games...
Problem 4. Two hockey teams, A and B play a series of games, until one of the teams wins 4 games. Suppose team A has probability p of winning each game, and games are independent. Let X be the total number of games that are played (a) Find the probability mass function of X (b) What is the probability that team A wins the series conditioned on X-47 (c) What is the probability that team A wins the series conditioned...
Problem 16-07 (Algorithmic) 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 are playing the Minnesota Twins 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...
Suppose that two teams play a series of games that ends when one of them has won 3 games. Suppose that each game played is, independently, won by team A with probability Let X be the number of games that are played. (a) Find P(X = 4) (b) Find the expected number of games played.
Problem 12-07 (Algorithmic) 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...
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