Question

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 the time, and loses 30% of the time. Given this, what is probability that it will win 3 games from now? C. If the team is coming off a losing streak of 3 games, what is the chance that it will not lose its next 2 games? D. The team travels on two different buses, and the travel times are exponentially-distributed with means µ1 and µ2 hours, respectively. Derive the probability of the first bus arriving first.

Answer #1

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A dodgeball team either wins, ties, or loses each game. If they
lose a game, their probability of winning the next game is 1 and
their probability of losing the next game is 0. If they tie a game,
their probability of winning the next game is 0.8 and their
probability of losing the next game is 0.1. If they win a game,
their probability of winning the next game is 0 and their
probability of losing the next game...

A local soccer team has 6 more games that it will play. If it
wins its game this weekend, then it will play its final 5 games in
the upper bracket of its league, and if it loses, then it will play
its final 5 games in the lower bracket. If it plays in the upper
bracket, then it will independently win each of its games in this
bracket with probability 0.3, and if it plays in the lower bracket,...

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?

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...

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?

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,...

5. A professional basketball team, has
won 12 of its last 20 games and it is expected to continue winning
at the same percentage rate. The team’s ticket manager is anxious
to attract a large crowd (filling the team’s basketball arena) to
next week’s game but believes that depends on how well the team
performs tonight against its rival. Based on her past experience,
she assese the probability of drawing a full-arena crowd to be 90
percent should the team...

Penny will play 2 games of badminton against Monica. Penny’s
chances of winning the first game is 70 % . If Penny wins the first
game then the chances to win the second game is 80% but if Penny
lose the first game then chances to win the second game is 50%.
Find the probability that Penny winning exactly one match.
First game Penny (A) win =
First game Monica (A) win =
Second game Penny (C) win...

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,...

JAVA: MUST BE DONE IN JAVA
Assignment: Write algorithms and programs to
play “non-betting” Craps. Craps is a game played with a pair of
dice. In the game, the shooter (the player with the dice)
rolls a pair of dice and the number of spots showing on the two
upward faces are added up. If the opening roll (called the
“coming out” roll) is a 7 (“natural”) or 11
(“yo-leven”), the shooter immediately wins the game. If
the coming out...

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