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Chapter 4: Q16 (page 143)
In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.
Sleepwalking Based on a report in Neurology magazine, 29.2% of survey respondents have sleepwalked.
The probability that a respondent of the survey has sleepwalked is 0.292.
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Complements and the Addition Rule Refer to the table used for Exercises 9–20. Assume that one order is randomly selected. Let A represent the event of getting an order from McDonald’s and let B represent the event of getting an order from Burger King. Find , find , and then compare the results. In general, does = ?
Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using a \(1 bill or a \)1 bill, college students were given either a \(1 bill or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).
Purchased Gum | Kept the Money | |
Students Given A \(1 bill | 27 | 46 |
Students Given a \)1 bill | 12 | 34 |
Denomination Effect
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
c. What do the preceding results suggest?
Rule of Complements When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements is telling us:
In Exercises 17–20, refer to the accompanying table showing results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources).
Positive Test Result | Negative Test Result | |
Hepatitis C | 335 | 10 |
No Hepatitis C | 2 | 1153 |
False Positive Find the probability of selecting a subject with a positive test result, given that the subject does not have hepatitis C. Why is this case problematic for test subjects?
Odds. In Exercises 41–44, answer the given questions that involve odds.
Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.
a. What is your probability of winning?
b. What are the actual odds against winning?
c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet \(18 and win?
d. How much profit would you make on the \)18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don’t actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)
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