QUESTION 1:

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),_._ D 1|Nhen we make inferences about ONE POPULATION PROPORTION, what assumptions do we need to make? Mark all that apply. a. Counts of successes and failures at least 15 each. o. The data must have a Normal Distribution. c. Data is quantitative. d. Counts of successes and failures at least 5 each. e. Data is categorical. f. Sample Size is 3D or more. g. Data must be from a simple random sample. 21:26 + 4 Search Collaborative Project weeks 1-3 MA.. Name: weeks 1-3 Probability Island You will collect the data for the population of an island community. Then you will use and evaluate probability models. You will be using this data for the next parts of your project. Your ship is carrying 150 passengers - 75 adult females and 75 adult males - all in good health, An intense storm occurs and your ship hits rocks and wrecks off the coast of a deserted island in the Pacific Ocean. This island has the necessary natural resources for human survival. The ages of your passengers are recorded in the table below Age Formain Main 26-39 10 Directions: Probability of births 1. For each woman aged 20-39, roll a die one time. If you get a 6, the woman has a baby. Flip a coin. If it's heads, it's a girl. If it's tails, it's a boy. Complete Chart 1 on the next page to track the births per year and the number of boys and girls. Repeat this simulation for ten years. Note: There are 20 women in these age groups. They are numbered 1 through 20 in the chart. For the purposes of this project, assume all women in these age groups remain capable of having children; keep everyone in their assigned age groups. 2. Assuming the births occur as recorded, and that no one dies, what is the population of your island at the end of the ten-year period? Use Chart 2 to clearly show the population of your island at the end of each year. 3. a. Calculate the theoretical probability and the experimental probability of the births. Show your work. b. Compare the theoretical probability to the experimental probability. C. Discuss any similarities and/or differences. You may consider the annual or gender rates or any other possibility. Chart 1. Woman Year 1 Year ? Year ] Toor & War S Tear Your Year Your War 4 7 8 9 10 30 Dashboard Calendar To Do Notifications inbox( Collaborative Project weeks 1-3 MA... Name: weeks 1-3 Probability Island You will collect the data for the population oi an island community. Then you will use and evaluate probabiiity models. You will be using this data for the next parts of yOur proied. Your ship is carrying 150 passengers - T5 adult females and 1'5 adult males all in good hearth. An intense storm occurs and your ship hlts rocks and melts on the coast of a deserted island In the Pacic Ocean. This Island has the necessary natural resources for human survival. The ages of your passengers are recorded in the table below. ~29 rundown 2-i2910 19 306910 it) 4.04910 it! 506915 15 60-6915 15 rm 15 ill Iolll T5 ?5 u. . 'E | 'I' i . 1. For each women aged 2039. roll a die one time. it you get a 6, the woman has a baby. Flip a coin. It It's heads. it's a girl. If it's tails, it's a boy. Complete Chart 1 on the next page to track the births per year and the number of boys and girls. Repeat this simulation for ten years. Note: There are 20 women in these age groups. They are numbered 1 through 20 in the chart. For the purposes of this PWiBEL assume all women in these age groups remain capable of having children: keep everyone in their assigned age groups. 2. Assuming the births occur as recorded. and that no one dies, whatls the population of your lsiand at the end oi the ten-year period? Use Chart 2 to clearly show the population of your island at the end of each year. 3. 3. Calculate the theaetical probability and the experimental probability of the births. Show your M. b. Conware the theoretical probability to the experimental probability. c. Discuss any similarities andior differences. You may oonsider the annual or gender rates or any other possibility. Chart 1. Warren Mr 1 Your 2 War 3hr o Year 5Wut'turmr Milan! 6 "i" B D ID I 2. Dashboard Calendar Inbox There are 20 women in these age groups. They are numbered 1 through 20 in the chart. For the purpom at this project assume all women in these age groups rernain capable at having children: keep everyone in their assigned age groups. 2. Assuming the births occur as recorded, and that no one dies, what is the population of your island at the end ot the ten-year period? Use Chart 2 In clearly show the population of your island at the end at each year. 3. a. Calculate the thmtical probability and the experimental probability of the births. Show your work. b. Compare the theoretical probability to the experimental probability. c. Discuss any similarities andi'or differences. You may consider the annual or gender rates or any other possibility. Chart 1. Winner! thzmawwmmwvwmmuw: - ? B B 1D natal Bills Chertz Year a vanssnoio Male r5 FVrI'i'S 'Felal