SECTION 3.4 Additional Topics in Probability and Counting 177 50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee. (a) Use technology to find the number of ways that 5 employees can be selected from 200. (b) Use technology to find the number of ways that 5 employees can be selected from 56 males. (c) Find the probability that no males will be selected by randomly selecting 5 of the 200 employees. Would this be a biased sample? Explain. (d) Explain how the company can select a representative sample of the male and female population of employees. Warehouse In Exercises 51–54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. 51. Find the probability of choosing five first-shift workers. 52. Find the probability of choosing three second-shift workers. 53. Find the probability of choosing four third-shift workers. 54. Find the probability of choosing two second-shift workers and two third-shift workers. Extending Concepts 55. Defective Units A shipment of 10 microwave ovens contains 2 defective units. A restaurant buys three units. What is the probability of the restaurant buying at least two nondefective units? 56. Defective Disks A pack of 100 recordable DVDs contains 5 defective disks. You select four disks. What is the probability of selecting at least three nondefective disks? 57. Employee Selection A company has eight sales representatives, two in each of four regions. The company randomly selects four of the eight representatives to participate in a training program. What is the probability that the four sales representatives chosen will be from only two of the four regions? 58. Employee Selection In Exercise 57, what is the probability that the four sales representatives chosen to participate in the training program will be from three of the four regions? Cards In Exercises 59– 62, you are dealt a hand of five cards from a standard deck of 52 playing cards. 59. Find the probability of being dealt two clubs and one of each of the other three suits. 60. Find the probability of being dealt four of a kind. 61. Find the probability of being dealt a full house (three of one kind and two of another kind). 62. Find the probability of being dealt three of a kind (the other two cards are different from each other).
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