Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.2.9

Chapter 4, Problem 4.2.9

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 one of the high school drivers is randomly selected, find the probability of getting one who drove when drinking alcohol.

Verified step by step guidance

Step 1: Understand the problem. The goal is to find the probability of randomly selecting a high school driver who drove when drinking alcohol. Probability is calculated as the ratio of favorable outcomes to the total number of outcomes.

Step 2: Identify the favorable outcomes. From the table, the number of high school drivers who drove when drinking alcohol is the sum of the 'Yes' column: 731 (Texted While Driving) + 156 (No Texting While Driving).

Step 3: Determine the total number of outcomes. The total number of high school drivers surveyed is the sum of all entries in the table: 731 + 3054 + 156 + 4564.

Step 4: Write the formula for probability. The probability of selecting a driver who drove when drinking alcohol is given by: \( P = \frac{\text{Number of drivers who drove when drinking alcohol}}{\text{Total number of drivers surveyed}} \).

Step 5: Substitute the values into the formula. Use the values calculated in Steps 2 and 3 to compute the probability. Simplify the fraction if necessary.

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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 refers to the chance of randomly selecting a high school driver who has driven after consuming alcohol. To calculate this, one would divide the number of drivers who drove after drinking by the total number of surveyed drivers.

Contingency Table

A contingency table is a type of data representation that displays the frequency distribution of variables. In this case, the table shows the relationship between texting while driving and driving after drinking alcohol. It helps in visualizing the data and is essential for calculating probabilities and understanding the associations between different behaviors.

Total Count

The total count refers to the sum of all observations in a dataset. For this question, it is crucial to determine the total number of high school drivers surveyed, which is the sum of all entries in the contingency table. This total is necessary for calculating the probability of selecting a driver who drove after drinking alcohol.

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