Skip to main content
Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.3.22b
Chapter 3, Problem 3.3.22b

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the
probability of each event. (Adapted from Ipsos)
b. Randomly selecting a British adult who feels that the move has had a very negative impact on Great Britain
Bar chart showing survey results on the impact of leaving the EU, with responses ranging from very negative to don't know.

Verified step by step guidance
1
Step 1: Identify the total number of respondents in the survey. According to the problem, the total number of British adults surveyed is 1115.
Step 2: Locate the number of respondents who feel that the move has had a 'very negative' impact. From the Pareto chart, this value is 256.
Step 3: Recall the formula for probability: \( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the favorable outcome is the number of respondents who feel the impact is 'very negative', and the total number of outcomes is the total number of respondents.
Step 4: Substitute the values into the formula: \( P(\text{Very Negative}) = \frac{256}{1115} \).
Step 5: Simplify the fraction if necessary to express the probability in its simplest form or as a decimal.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

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 British adult who perceives the impact of Brexit as 'very negative.' This can be calculated by dividing the number of respondents who selected 'very negative' by the total number of respondents.
Recommended video:
5:37
Introduction to Probability

Pareto Chart

A Pareto chart is a type of bar graph that represents the frequency or impact of problems in a descending order. It helps to visualize the most significant factors in a dataset. In this case, the chart displays the responses of British adults regarding the impact of Brexit, allowing for easy identification of the most common perceptions.
Recommended video:
04:52
Creating Bar Graphs and Pareto Charts

Survey Sampling

Survey sampling involves selecting a subset of individuals from a larger population to gather insights about that population. In this scenario, 1,115 British adults were surveyed to understand their views on Brexit. The sample size is crucial for ensuring that the results are representative and can be generalized to the broader population.
Recommended video:
05:11
Sampling Distribution of Sample Proportion
Related Practice
Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

b. Find the probability that neither probable voter would like entertainers to address social and political issues."

Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

30. Standardized Test Scores According to a survey, 57.8% of college-seeking high school seniors say they have taken one of the standardized tests for potential college students. Of these, 35.6% say they do not plan to submit their score with their college applications. (Adapted from Niche)

b. Find the probability that a randomly selected college-seeking high school senior took one of the standardized tests and plans to submit this score with their college

applications.

Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

28. Blood Types The probability that a Latinx American person in the United States has type A+ blood is 29%. Four Latinx American people in the United States are selected at random. (Source: American National Red Cross)

b. Find the probability that none of the four have type A+ blood.

Textbook Question

Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

8. Retirement Savings The table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at

work.

b. Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work.

Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. b. 333.3%

Textbook Question

Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team.

b. What is the probability that none of the offices are filled by members of the debate team?