Two basketball teams (the Celtics and the Lakers) are set to play a series of n...
Two basketball teams (the Celtics and the Lakers) are set to play a series of n basketball games, where we assume that n is odd. The Celtics have a probability p of winning any one game, independent of the other games. The Celtics win the series if they win the majority of the games.
(a) For which values of p is Pr(Celtics win series | n = 5) > Pr(Celtics win series | n = 3)?
(b) For which values of p is Pr(Celtics win series | n = 11) > Pr(Celtics win series | n = 9)?
(Bonus) For which values of p is Pr(Celtics win series | n = 2k-1) > Pr(Celtics win series | n = 2k+1)?
Although I have seen some answers, I need more details about the procedure.
Homework Answers
Add Answer to:
Two basketball teams (the Celtics and the Lakers) are set to
play a series of n...
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
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...
Suppose two teams are playing a series of games, each of which is independent. Team A...
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...
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...
2. Are the teams that play in the World Series evenly matched? To win a World...
2. Are the teams that play in the World Series evenly matched? To win a World Series, a team must win four games. If the teams are evenly matched, we would expect the number of games played in the World Series to follow the distribution shown in the first two columns of the following table. The third column represents the actual number of games played in each World Series from 1930 to 2014. Do the data support the distribution that...
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.
Two baseball teams engage in a playoff series in which the series is won by the...
Two baseball teams engage in a playoff series in which the series is won by the first team to win 4 games. If each team is equally likely to win any game, what is the expected number of games played?
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.
Question 2 (26 points) In an NBA (National Basketball Association) series, the team that wins four...
Question 2 (26 points) In an NBA (National Basketball Association) series, the team that wins four games out of seven is the winner and it will win the big prize. Suppose that teams A and B face each other in the games and that team A has probability 0.4 of winning a game over team B. a) (13 points) Compute the probability that team A wins the big prize at (just after) the 6"game. b) (13 points) Compute the probability...
math 5. One year, the A's play the B's in the World Series, a seven-game series...
math
5. One year, the A's play the B's in the World Series, a seven-game series of baseball games. The World Series winner is the team that wins at least four games.1 Suppose that all games are independent and for each game, the probability that the A's win is p (which is the same for each game.) We don't know the exact value of p, but it's estimated that in professional baseball, the better team wins between 50% and 70%...
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...
2. Are the teams that play in the World Series evenly matched? To win a World Series, a team must win four games. If the teams are evenly matched, we would expect the number of games played in the World Series to follow the distribution shown in the first two columns of the following table. The third column represents the actual number of games played in each World Series from 1930 to 2014. Do the data support the distribution that...
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.
Question 2 (26 points) In an NBA (National Basketball Association) series, the team that wins four games out of seven is the winner and it will win the big prize. Suppose that teams A and B face each other in the games and that team A has probability 0.4 of winning a game over team B. a) (13 points) Compute the probability that team A wins the big prize at (just after) the 6"game. b) (13 points) Compute the probability...
math
5. One year, the A's play the B's in the World Series, a seven-game series of baseball games. The World Series winner is the team that wins at least four games.1 Suppose that all games are independent and for each game, the probability that the A's win is p (which is the same for each game.) We don't know the exact value of p, but it's estimated that in professional baseball, the better team wins between 50% and 70%...
Most questions answered within 3 hours.
-
Brooke and Georgia are neighbors. Each have 40 hours per week.
Brooke needs 5 hours to...
asked 29 minutes ago -
Quantitative Problem: You are holding a
portfolio with the following investments and betas:
Stock
Dollar investment...
asked 26 minutes ago -
Within the costing system of a manufacturing company the
following types of expenses were incurred:
Details...
asked 29 minutes ago -
Data from the Bureau of Labor Statistics’ Consumer Expenditure
Survey show that annual expenditures for cellular...
asked 45 minutes ago -
Consider the following MIPS code:
add $t3,$t2,$t1
lw $t4,0($t3)
sw $t7,0($t3)
add $t6,$t2,$t8
addi $t3,$t5,4
(a)...
asked 41 minutes ago -
Assembly Language:
Is it TRUE or FALSE:
Reduced Instruction Set Computers (RISC) are characterized
by:
Relatively...
asked 45 minutes ago -
A ball is thrown from the origo over a flat horizontal ground.
the x-axis is
horizontal...
asked 47 minutes ago -
Discuss graph representation, Breadth-first search and
Depth-first search. Use examples to highlight pros and
cons.
asked 54 minutes ago -
what are the impacts of droughts in east Africa on the:
1) economy:
2) agriculture:
3)...
asked 56 minutes ago -
Fleas can jump quite high; experiments show that they can reach
an altitude of 120 times...
asked 1 hour ago -
The rate constant for this first-order reaction is 0.0520 s–1 at
400 °C.
A----> Product
After...
asked 1 hour ago -
boolean a = ( true && false );
System.out.println( a );
what is the output of...
asked 1 hour ago