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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 3.3.21d
Chapter 3, Problem 3.3.21d

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)
d. Randomly selecting a person from the sample who is either unsure or moderate

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Step 1: Understand the problem. The goal is to find the probability of randomly selecting a person from the sample who is either 'unsure' or 'moderate'. This involves adding the probabilities of these two categories.
Step 2: Identify the total number of respondents in the survey, which is given as 1500. This will serve as the denominator for calculating probabilities.
Step 3: From the Pareto chart, determine the number of respondents in the 'unsure' category and the 'moderate' category. These values will serve as the numerators for their respective probabilities.
Step 4: Add the counts of the 'unsure' and 'moderate' categories together to find the total number of respondents who fall into either of these two categories.
Step 5: Divide the total number of respondents in the 'unsure' or 'moderate' categories by the total number of respondents (1500) to calculate the probability. Use the formula: \( P(\text{unsure or moderate}) = \frac{\text{Number of unsure or moderate respondents}}{\text{Total respondents}} \).

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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 of randomly selecting a person from a sample who falls into specific categories, such as 'unsure' or 'moderate' political viewpoints. Understanding how to compute probabilities based on survey data is essential for answering the question.
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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, highlighting the most significant factors. In this case, the chart displays the political viewpoints of the surveyed individuals, allowing for a visual assessment of how many respondents identify as 'unsure' or 'moderate.' Familiarity with interpreting Pareto charts is crucial for extracting relevant data for probability calculations.
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Creating Bar Graphs and Pareto Charts

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. For this question, it refers to the total number of respondents in the survey, which is 1500. Understanding the sample space is vital for calculating the probability of selecting individuals with specific characteristics, as it provides the denominator for probability calculations.
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Related Practice
Textbook Question

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

25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.

(Adapted from YouGov)

d. Which of the events can be considered unusual? Explain.

Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

d. The person is male or does not wear glasses.

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Textbook Question

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

26. Worst President In a sample of 1500 adult U.S. citizens, 690 said that Donald Trump was the worst president in U.S. history. Three adult U.S. citizens are selected at random.

(Adapted from YouGov)

c. Find the probability that at most two of the three adult U.S. citizens say that Donald Trump was the worst president in U.S. history.

Textbook Question

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)

d. Randomly selecting a British adult who feels that the move has had a fairly positive or very positive impact on Great Britain

Textbook Question

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

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

c. Find the probability that at least one of the six has type O+ blood.

Textbook Question

Mental Health A survey asks 4805 parents the severity of the mental issues they experienced from the coronavirus pandemic. The results are shown in the table. A parent is randomly selected from the sample. Find the probability of each event. (Adapted from Kaiser Family Foundation)

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c. The parent did not have major mental health issues or is a mother.

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