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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 4, Problem 4.2.20

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.
"Table showing high school drivers' texting and drinking habits: 731 texted and drank, 3054 texted only, 156 drank only, 4564 neither."
Texting and Alcohol If four different high school drivers are randomly selected, find the probability that they all texted while driving.

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Step 1: Calculate the total number of high school drivers surveyed. Add all the values in the table: 731 + 3054 + 156 + 4564.
Step 2: Determine the total number of drivers who texted while driving. Add the values in the 'Texted While Driving' row: 731 + 3054.
Step 3: Calculate the probability of randomly selecting one driver who texted while driving. Divide the total number of drivers who texted while driving by the total number of drivers surveyed: P(Texted While Driving) = (731 + 3054) / (Total Drivers).
Step 4: Since four drivers are randomly selected, use the multiplication rule for independent events to find the probability that all four texted while driving. Multiply the probability of texting while driving by itself four times: P(All Four Texted) = P(Texted While Driving)^4.
Step 5: Ensure that the assumption of independence is valid. Verify that the selection of one driver does not affect the probability of selecting another driver who texted while driving.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance that all four randomly selected high school drivers texted while driving. This requires understanding how to compute probabilities for independent events, where the outcome of one event does not affect the others.
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Introduction to Probability

Independent Events

Independent events are those whose outcomes do not influence each other. In this scenario, selecting one driver who texted while driving does not change the probability of the next driver also texting. This concept is crucial for calculating the overall probability of multiple drivers texting, as it allows us to multiply the individual probabilities together.
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Probability of Multiple Independent Events

Sample Space

The sample space is the set of all possible outcomes of a probability experiment. For this question, it includes all high school drivers categorized by their texting and drinking behaviors. Understanding the sample space helps in determining the total number of drivers who texted while driving, which is essential for calculating the probability of selecting four drivers who all texted.
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Sampling Distribution of Sample Proportion
Related Practice
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Textbook 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.

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