Suppose four teams, numbered one through four, play a single-elimination tournament, consisting of three games. Two...

Suppose four teams, numbered one through four, play a single-elimination tournament, consisting of three games. Two teams play each game and one of them wins; ties do not occur. The tournament bracket is as follows: teams one and another team play each other in the first game and the remaining two teams play each other in the second game; the winner of the first game plays the winner of the second game in the third game.

Define a set ΩΩ so the elements of ΩΩ correspond to the possible outcomes of the tournament. An element of ΩΩspecifies the entire sequence of outcomes of the games. How many outcomes are there for the combination of what bracket is used and the game outcomes? (Assume the order the two games are played in the first round does not matter. For example, they could be simultaneous.)

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Teams A and B play in a basketball tournament. The first team to win two games...

Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of three games wins the tournament. What is the number of ways the tournament can occur? 14 12 8 10 How many different rearrangements are there of the letters in the word BUBBLE? 60 100 120 80 How many ways are there to arrange all the words in this tongue twister? CAN YOU CAN A CAN AS A...

A plays B in a tournament. The one who wins three games first gets the tournament...

A plays B in a tournament. The one who wins three games first gets the tournament trophy. In each game, A's chance of winning is 0.75. Both A and B perform independently from game to game and there is no draw for any game. a) Use a negative binomial distribution to calculate the probability that A gets the tournament trophy b) Use a binomial distribution to calculate the probability that A gets the tournament trophy.

2. Consider a two-team league in which the teams play 100 games. The large market team...

2. Consider a two-team league in which the teams play 100 games. The large market team gets gate revenue 12w – (w2/20) if it wins w games while the small market team gets 8w – (w2/20) if it wins w games. There are no other sources of revenue. i) Find the equilibrium number of wins for each team and the marginal cost of a win. ii) Suppose that there is revenue sharing, with each team keeping 50% of its revenue...

Consider a best-of-seven series. Two teams A and B play one another until one of the...

Consider a best-of-seven series. Two teams A and B play one another until one of the teams wins 4 games. The games are played indepedently, and the probability of team A winning any game is 2/3. a. Find the expected number of games the series lasts. b. Find the expected number of games team A wins. c. Find the expected number of games team B wins. d. Find the probability of team B winning the series.

Two team (A and B) play a series of baseball games. The team who wins three...

Two team (A and B) play a series of baseball games. The team who wins three games of five-game-series wins the series. Consider A has home-field advantage (0.7 means A has probability of winning 0.7 if it plays in its field) and opponent-field disadvantage (0.2 means A has probability of winning 0.2 if it plays in opponents field). If the series start on A team’s field and played alternately between A and B team’s fields, find the probability that series...

Two baseball teams play a best-of-seven series, in which the series ends as soon as one...

Two baseball teams play a best-of-seven series, in which the series ends as soon as one team wins four games. The first two games are to be played on A’s field, the next three games on B’s field, and the last two on A’s field. The probability that A wins a game is 0:7 at home and 0:5 away. Assume that the results of the games are independent. Find the probability that: (a) A wins the series in 4 games;...

QUESTION 3 Suppose the one-year, two-year, three-year, and four-year spot rates are determined to be 1%,...

QUESTION 3 Suppose the one-year, two-year, three-year, and four-year spot rates are determined to be 1%, 2%, 3%, and 4%, respectively. What is the yield to maturity of a four-year, 5% annual coupon paying bond? a. 3.467% b. 3.878% c. 3.964%

Suppose two players play the following prisoner's dilemma for 10 periods (periods 1 through 10). C...

Suppose two players play the following prisoner's dilemma for 10 periods (periods 1 through 10). C D C 3,3 -1,4 D 4,-1 0,0 Suppose that players simultaneously choose their strategy before the repeated game, and can't change it once the repeated game has started. Players can choose one of the three following strategies as defined in class: • Always Defect • Grim-Trigger • Tit-For-Tat (a) Draw the 3×3 matrix game with the payoffs for each strategy pair calculated over the...

A bag contains four red marbles, two green ones, one lavender one, three yellows, and three...

A bag contains four red marbles, two green ones, one lavender one, three yellows, and three orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

Suppose that you shine light from a laser through two slits that are placed one in...

Suppose that you shine light from a laser through two slits that are placed one in front of the other, separated by 0.6mm. The width of each slit is 0.12mm. The light will travel from the laser, through the slits, and onto a screen 1.5m away. a. Predict what you will observe on the screen, and compare it to what you would expect from single-slit diffraction. b. If ray (geometrical optics) accurately described this siutation, what would the pattern on...

Subjects