High Fives


b. If n mathletes shake hands with each other exactly once, what is the total number of handshakes?

Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a \$1 bill, some college students were given four quarters and others were given 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).

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given a \)1 bill.

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting While Driving If two of the high school drivers are randomly selected, find the probability that they both texted while driving.

a. Assume that the selections are made with replacement. Are the events independent?

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Drinking and Driving If two of the high school drivers are randomly selected, find the probability that they both drove when drinking alcohol.

b. Assume that the selections are made without replacement. Are the events independent?

In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.

Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).

b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter?

Mega Millions As of this writing, the Mega Millions lottery is run in 44 states. Winning the jackpot requires that you select the correct five different numbers from 1 to 70 and, in a separate drawing, you must also select the correct single number from 1 to 25.

a. Find the probability of winning the jackpot.