A bookmaker is attempting to calculate the odds of a football team winning the next three matches (match A, match B and match C). They determine the probability of the team winning each respective match to be                P(A) =0.35  ;    P(B) =  0.65 ;   P(C) = 0.58 Assuming that these three events are independent, determine the probability that the team will(i) win all three matches      (Give your answer correct to 3 decimal places)                                                                                    (ii) win at least one match   (Give your answer correct to 3 decimal places)

In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called “best of 5”]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played? 0.50 0.25 0.20 0.125

A,B and C play a game and the chances of their winning it in an attempt are (2/3), (1/2) and (1/4) respectively. A has the first chance, followed by B and then by C. This cycle is repeated till one of them wins the game. Then the probability that B wins is

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.

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 certain online computer game, there are 55 players on the Green Team and 100 players total in the game.The game randomly chooses a player to receive a bonus. Let the event A and the event B be as follows.A: The player the game chooses is on the Green Team.B: The player the game chooses is not on the Green Team.Find the following probabilities. Write your answers as decimal numbers and do not round.=PA=PB