An eight-team single-elimination tournament is set up as follows: For example,eight students (called A,B,...,H) set up a tournament among themselves. The top-listed2student in each bracket calls heads or tails when his or her opponent flips a coin. If the callis correct, the student moves on to the next bracket.(a) How many coin flips are required to determine the tournament winner?(b) What is the probability that you can predict all of the winners?(c) In NCAA Division I basketball, 64 teams participate in a single-elimination tourna-ment to determine the national champion. How many games are required to determine thenational champion?(d) Assume that for any given game, either team has an equal chance of winning (thatis probably not true). On page 43 of the March 22, 1999, issue, Time claimed that the“mathematical odds of predicting all 63 NCAA games correctly is 1 in 75 million.” Do youagree with this statement? If not, why not?

Two evenly matched basketball teams (call them A and B) compete in a best-of 7 championships (the first team to win 4 games wins the championship). Once the champion has been determined, no more games are played. In each game, there is a home team and an away team. The home team wins the game with probability p ≥ 1/2, independent of all previous games. Suppose that the first three games will be held at the home of team A and the last 4 (or fewer if they are not needed) are played at the home of team B.(a) Let X be the number of games won by team A out of the first 3 games. Specify the distribution of X.(b) Find the probability that only 4 games are played.(c) Which of the two teams is more likely to win the trophy? Explain why.(d) Give an expression for the probability that team A wins the trophy, and evaluate it when p = 0.55.(e) Let Y be the number of games won by team A. Find the probability mass function for Y.(f) Evaluate the expected number of games won by team A and the expected number of games played when p = 1/2.(g) Observe (via computations or simulation) that when p = 0.55 the expected number of games won by team A is larger than that of team B, even though team B is more likely to win the trophy.

You will create an algorithm to determine the winner of each game in the NCAA men's basketball bracket (at least for the east and west regions). Your code does not necessarily need to determine the winner of the entire tournament, but simply work on a game by game basis. Basically, the user should be able to enter the two teams and the code will use the provided lists to determine the winner.Your code should:involve an algorithm that determines a winner between two teamshave a way to determine the winner of a tieuse the given data (at least 2 pieces of data per team)ask for the next match-up after determining a winner (or if you are done)reject any typos or names not in the tournamentinclude commentscreate a new list:it will store the number of wins for each team (Hint this can be done very quickly and easily with a loop.)this list should be mutable and change as you enter match-upsthis list will print once you are done entering match-upsYOU DO NOT HAVE TO KNOW ANYTHING ABOUT BASKETBALL TO DO THIS!! For those of you who are college basketball fans, you should know about bracketology and your algorithm will probably be more precise. If you have no idea about basketball or sports in general, ITS OK! You should know that when two people compete, there is a winner. You will simply pick some data to use in an algorithm to determine a winner. I am not grading this on accuracy to the real games.

Look at page 2 of the Article. Drag the events to put them in the order in which they happen.HINT1.Teams are assigned to repair a car with a deliberately rigged problem.2.The top 10 pairs advance to the state finals.3.Teams take a 100-question written exam.4.Teams of two take an online examination.5.The top pair from each state goes to the national finals.SUBMITExtras

6) It is the last week of the football season. In order for the Knights to make the playoffs, the Knights must win and the Cougars must lose. The Knights and the Cougars do not play against each other. P (Knights win) = 0.75 P (Cougars lose) = 0.40 a) Are the events "Knights Win" and "Cougars Lose" independent? Justify your answer. b) What is the probability that the Knights will make the playoffs? Show how you determined your answer. 7) There are three boys in a class of nine students. Three students are to be randomly selected (without replacement) to help with bus duty. Determine the probability that all three students are boys. Show how you determined your answer.

In a tournament, a team has played 40 matches so far and won 30%30% of them. If they win 60%60% of the remaining matches, their overall win percentage will be 50%50%. Suppose they win 90%90% of the remaining matches, then the total number of matches won by the team in the tournament will be.