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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 4 - ProbabilityProblem 4.2.11
Chapter 4, Problem 4.2.11

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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Step 1: Understand the problem. We are tasked with finding the probability of selecting a high school driver who either texted while driving or drove when drinking alcohol. This involves calculating the union of two events: 'Texted While Driving' and 'Drove When Drinking Alcohol.'
Step 2: Identify the relevant data from the table. The table provides the counts for four categories: (1) Texted While Driving and Drove When Drinking Alcohol (731), (2) Texted While Driving and Did Not Drive When Drinking Alcohol (3054), (3) Did Not Text While Driving and Drove When Drinking Alcohol (156), and (4) Did Not Text While Driving and Did Not Drive When Drinking Alcohol (4564).
Step 3: Calculate the total number of high school drivers surveyed. Add all the values in the table: 731 + 3054 + 156 + 4564. This gives the total sample size.
Step 4: Use the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Here, A is 'Texted While Driving,' B is 'Drove When Drinking Alcohol,' and A ∩ B is 'Texted While Driving and Drove When Drinking Alcohol.'
Step 5: Compute the individual probabilities. Divide the counts for each event by the total sample size: P(A) = (731 + 3054) / Total, P(B) = (731 + 156) / Total, and P(A ∩ B) = 731 / Total. Substitute these values into the formula from Step 4 to find the probability of the union of the two events.

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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 an event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of randomly selecting a high school driver who either texted while driving or drove after drinking alcohol. Understanding how to compute probabilities from a contingency table is essential for answering the question.
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Introduction to Probability

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 under the influence of alcohol. Analyzing the table helps in determining the total counts and the specific counts needed to calculate the desired probabilities.
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Finding Standard Normal Probabilities using z-Table

Union of Events

The union of events refers to the occurrence of at least one of the events in question. For this problem, it involves finding the probability that a randomly selected driver either texted while driving or drove after drinking. This requires using the formula for the union of two events, which combines their individual probabilities while accounting for any overlap.
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Related Practice
Textbook Question

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.



Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

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Textbook Question

Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

15.53 7.27 7.45 10.39 4.70 4.50 3.44 5.70 8.24 7.30 4.05 4.46


a. mean

b. median

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Textbook Question

Combination Lock The typical combination lock uses three numbers, each between 0 and 49. Opening the lock requires entry of the three numbers in the correct order. Is the name “combination” lock appropriate? Why or why not?

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Textbook Question

Notation When randomly selecting a new smartphone, D denotes the event that it has a manufacturing defect. What do P(D) and P(D) represent?

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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 and Alcohol If four different high school drivers are randomly selected, find the probability that they all texted while driving.

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Textbook Question

Heights of Presidents Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runners up. Listed below are heights (cm) from recent presidential elections. Construct a graph suitable for exploring an association between heights of presidents and the heights of the presidential candidates who were runners-up. What does the graph suggest about that association?

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