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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 4 - Probability문제 4.2.11
4장, 문제 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.

검증된 단계별 안내
1
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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주요 개념

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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.
추천 영상:
5:37
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.
추천 영상:
가이드 코스
09:47
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.
추천 영상:
05:54
Probability of Multiple Independent Events
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교과서 질문

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

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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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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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교과서 질문

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