In Exercises 9–20, use the data in the following table, which ...

Question

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 or Drinking If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

Texting or Drinking If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

Accepted Answer

All right, hello, everyone. So this question says, a study recorded the responses of 8,505 office employees regarding headphone use and reports of ear discomfort. The results are summarized in the table below. If one of the employees is randomly selected, what is the probability that the person either used headphones frequently or reported ear discomfort? Option A says. 0.040, B is 0.005, C is 0.552, and option D is 0.460. So, for the sake of simplicity, right, let's say that capital A represents the probability of people that use headphones frequently. And let's say that capital B is the probability of individuals reporting ear discomfort. What's important to recognize in this question is that we're looking for the probability of either A or B, but not both of them at the same time. So because of that, we're going to use the general addition rule for probabilities, which says that the probability of either A or B. Is equal to The sum of either probability individually, that is the probability of A added to the probability of B. Subtracted by the probability of A and B. Because to solve for the probability of either or, you have to remove the probability of obtaining both. So let's use the given table to extract the information that we need, starting off with A. So, the individuals in total that reported ear discomfort. Or rather that use headphones frequently because we're solving for a. Is the sum of 782 and 2,986. Because here you have to account for the people that use headphones frequently, whether or not they experience ear discomfort. So, the probability of A. Is equal to the sum of both numbers, which is 3,768. And then divided by the total number of participants, which in this case was the 8,505 employees. Now for the probability of B you would do the same thing, right, but this time you would look for the number of people that reported ear discomfort. Whether or not they used headphones frequently. So looking at those values in the table, that's 782 added to 143. Which equals 925, and the denominator is the same as before. So that's 8,505. Last but not least, right, we want to find the probability of people that have experienced ear discomfort and wear headphones frequently. So looking for that value in the data table. That gives you 782. Because that's the number of people that reported both. So you would subtract the sum of both individual probabilities by. That's 782 divided by 8,505. And so after evaluating this expression. You obtain the probability of A or B. Which ultimately equals approximately 0.460. Meaning that option D is the correct answer choice. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Probability

Contingency Table

Union of Events

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