CHAPTER 11 Review Exercises 757 If one person who completed the survey is randomly selected, determine the probability that the person indicated that the 39. service was rated poor. 3 20 40. service was rated good, given that the meal was lunch. 5 6 41. service was rated poor, given that the meal was breakfast. 3 22 42. meal was breakfast, given that the service was rated poor. 1 2 Neuroscience In Exercises 43– 46, assume that in a neuroscience course the students perform an experiment. Tests are given to determine if people are right brained, are left brained, or have no predominance. It is also recorded whether they are right handed or left handed. The following chart shows the results obtained. Right Brained Left Brained No Predominance Total Right handed 40 130 60 230 Left handed 120 30 20 170 Total 160 160 80 400 If one person who completed the survey is randomly selected, determine the probability the person selected is 43. right handed. 23 40 44. left brained, given that the person is left handed. 3 17 45. right handed, given that the person has no predominance. 3 4 46. right brained, given that the person is left handed. 12 17 47. Game Show Four contestants are on a game show. There are four different-colored rubber balls in a box, and each contestant gets to pick one ball from the box. Inside each ball is a slip of paper indicating the amount the contestant has won. The amounts are $10,000, $5000, $2000, and $1000. a) In how many different ways can the contestants select the balls? 24 b) What is the expectation of a contestant? $4500 48. Spelling Bee Five finalists remain in a high school spelling bee. Two will receive $50 each, two will receive $100 each, and one will receive $500. How many different arrangements of prizes are possible? 30 49. Cereal Selection Mrs. Williams takes her 3 children shopping. Each of her children gets to select a different type of cereal that only that child will eat. At the store, there are only 10 boxes of cereal left and each is a different type. In how many ways can the 3 children select the cereal? 720 50. Astronaut Selection Three of nine astronauts must be selected for a mission. One will be the captain, one will be the navigator, and one will perform scientific experiments. Assuming each of the nine astronauts can perform any of the tasks, in how many ways can a three-person crew be selected so that each person has a different assignment? 504 51. Vaccine Dr. Goldberg has three doses of vaccine for influenza type A. Six patients in the office require the vaccine. In how many different ways could Dr. Goldberg dispense the vaccine? 20 52. Dogsled Ten huskies are to be selected to pull a dogsled. How many different arrangements of the 10 huskies on a dogsled are possible? 3,628,800 53. Mega Millions To play the lottery game Mega Millions, you select 5 numbers, in any order, from 1 through 70 and 1 Mega Ball number from 1 through 25. If you match all 6 numbers, you win the jackpot! a) What is the probability that you match the first 5 numbers? 1 12,103,014 b) What is the probability that you match the first 5 numbers and the Mega Ball? 1 302,575,350 54. Parent-Teacher Committee A committee of 7 is to be formed from 10 parents and 12 teachers. If the committee is to consist of 2 parents and 5 teachers, how many different committees are possible? 35,640 55. Selecting Test Subjects In a psychology research laboratory, one room contains eight men and another room contains five women. Three men and two women are to be randomly selected to be given a psychological test. How many different selections of these people are possible? 560 56. Choosing Two Aces Two cards are dealt without replacement, from a standard 52-card deck. Determine the probability that two aces are selected (use combinations). 1 221 + Mega Millions win Select Mega Ball number from 1–25 Select 5 numbers from 1–70
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