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.
X and Y play a series of games. X has a probability p of winning each...
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 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...
A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1−p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the grater number of total wins is declared the winner of the series. Find the probability that a total of 4 games are played. Please explain as much as possible.
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...
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
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.
Each game you play, you win with probability p, 0<p<1. You plan to play 5 games, but if you win the fifth game, you will keep playing until you lose. Assume the outcome of each game is independent of all others. a) Find the expected number of games you loss. b) Find the expected number of games you win.
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 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...
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...