228 CHAPTER 5 Discrete Probability Distributions Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula. 13. Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions. a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third is correct. That is, find P(WWC), where W denotes a wrong answer and C denotes a correct answer. b. Beginning with WWC, make a complete list of the different possible arrangements of two wrong answers and one correct answer, and then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made? 14. Porch Pirates An InsuranceQuotes.com survey showed that 8% of Americans had a holiday package stolen from outside their front door. Consider the random selection of four Americans. a. Use the multiplication rule to find the probability that the first three did not have a package stolen from outside their front door and the fourth subject did have a package stolen from outside their front door. That is, find P(NNNS), where N denotes that no package was stolen and S indicates that a package was stolen. b. Beginning with NNNS, make a complete list of the different possible arrangements of those four letters, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly three Americans who did not have a package stolen from outside their front porch and one American who did have a package stolen from outside their front porch. Cashless Society. 40% of consumers believe that cash will be obsolete in the next 20 years (based on a survey by J.P. Morgan Chase). In each of Exercises 15–20, assume that 8 consumers are randomly selected. Find the indicated probability. 15. Find the probability that exactly 6 of the selected consumers believe that cash will be obsolete in the next 20 years. 16. Find the probability that at least 6 of the selected consumers believe that cash will be obsolete in the next 20 years. 17. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. 18. Find the probability that no more than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. 19. Find the probability that none of the selected consumers believes that cash will be obsolete in the next 20 years. 20. Find the probability that at least one of the selected consumers believes that cash will be obsolete in the next 20 years. In Exercises 21–24, assume that when human resource managers are randomly selected, 65% of them say that after submitting a résumé, job applicants should follow up within two weeks. 21. If 10 human resource managers are randomly selected, find the probability that exactly 6 of them say job applicants should follow up within two weeks. 22. If 16 human resource managers are randomly selected, find the probability that exactly 12 of them say job applicants should follow up within two weeks. 23. If 20 human resource managers are randomly selected, find the probability that at least 18 of them say job applicants should follow up within two weeks. 24. If 14 human resource managers are randomly selected, find the probability that fewer than 3 of them say job applicants should follow up within two weeks.
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