SET A:
1. A club has 21 members, four of whom are executives. Five members are randomly selected to take part in a survey. a) What is the probability that four non-executive members are chosen? b) What is the expected number of non-executive members?(four marks)2. State which type of distribution (uniform, binomial, hypergeometric, none of these) would model each situation. (six marks) a) Drawing eight names out of a hat without replacement and recording the number of females. b) Generating random numbers between 1 and 100 and recording the number of prime numbers in 20 trials. c) Selecting the winning ticket in a raffle. d) Noting the wait time before you reach the front of a line. e) Recording the number of doubles when rolling two standard dice. f) Recording when the first occurrence of a red jelly bean occurs while selecting jelly beans from a bag.3. A card is repeatedly cut from a standard deck, with replacement, for a total of five cuts. The number of aces is recorded.(four marks) a) Is this a binomial or hypergeometric distribution? Why? b) Rewrite the situation to convert it to a hypergeometric or binomial distribution, as appropriate.4. A total of 5000 tickets were sold for a raffle. The prizes are $1000, $500, $200, and $100. What price should be charged so there is a 60% profit per ticket?(four marks)5. A hockey league holds its annual player draft. The five worst teams from the previous season have a chance to draft first to fifth through a lottery, with more chances for the worse teams. The Panthers get 5 balls, the Wolves get 4 balls, the Kings get 3 balls, the Blues get 2 balls, and the Ducks get 1 ball. a) One ball is drawn to determine which team gets the first pick. Show the probability distribution for each team getting the first pick. b) To determine which team gets the second pick, all the remaining balls of the team that got the first pick are removed, and another ball is picked. What is the probability that the Kings get the first pick and the Panthers get the second pick? c) This process continues until all five picks are made. What is the probability that the teams get their picks in the order written above? d) What is the probability that the Wolves get the second pick? (five marks)6. A lottery has 5 000 000 tickets and each ticket costs $2.00. The table shows the prizes available. Prize ($) Number of Prizes 1 000 000 250 000 2 50 000 10 1 000 50 100 500 10 1 000 5 10 000 What is the expected value of each ticket?(five marks)
