Textbook Question
18. Rolling a Die You roll a die. Find the probability of each event.
b. Rolling a 2 or an odd number
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Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.2.26b
"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)
b. Find the probability that none of the three adult U.S. citizens say that Donald Trump was the worst president in U.S. history."
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability that none of the three randomly selected adult U.S. citizens say that Donald Trump was the worst president in U.S. history. This involves using the Multiplication Rule for independent events.
Step 2: Calculate the probability that a single adult U.S. citizen does NOT say that Donald Trump was the worst president. From the sample, 690 out of 1500 said he was the worst president. Therefore, the probability that a single person does NOT say this is given by \( P(\text{not worst}) = 1 - \frac{690}{1500} \).
Step 3: Recognize that the three selections are independent events. The probability that none of the three selected individuals say that Donald Trump was the worst president is the product of the probabilities for each individual.
Step 4: Use the Multiplication Rule. Multiply the probability of \( P(\text{not worst}) \) for each of the three individuals: \( P(\text{none say worst}) = P(\text{not worst}) \times P(\text{not worst}) \times P(\text{not worst}) \).
Step 5: Simplify the expression. Substitute the value of \( P(\text{not worst}) \) from Step 2 into the formula from Step 4 and simplify to find the final probability.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Multiplication Rule of Probability
The Multiplication Rule states that the probability of two or more independent events occurring together is the product of their individual probabilities. In this context, it helps calculate the likelihood of multiple citizens independently expressing the same opinion about Donald Trump being the worst president.
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05:17
Multiplication Rule: Dependent Events
Independent Events
Independent events are those whose outcomes do not affect each other. In this scenario, the selection of one adult citizen does not influence the opinions of the others, allowing us to treat their responses as independent when calculating probabilities.
Recommended video:
05:54Probability of Multiple Independent Events
Complementary Probability
Complementary probability refers to the likelihood of an event not occurring. In this case, to find the probability that none of the three selected citizens say Trump is the worst president, we first determine the probability that one citizen does not hold that opinion and then apply the Multiplication Rule to find the overall probability for three citizens.
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4:23Complementary Events
Related Practice
Textbook Question
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)
a. Find the probability that all four have lost a friend or relative to murder.
Textbook Question
Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.
7. Business Degrees The table shows the numbers of male and female students in the United States who received bachelor's degrees in business and nonbusiness fields in a recent year. (Source: National Center for Educational Statistics)
b. Find the probability that a randomly selected bachelor's degree-earning student received a business degree, given that the student is female.
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Textbook Question
Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the
probability of each event. (Source: American College Health Association)
a. Randomly selecting a student who never used marijuana
Textbook Question
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
29. In Vitro Fertilization In a recent year, about 1.9% of all infants born in the U.S. were conceived through assisted reproductive technology (ART). Of the ART deliveries, about 26.4% resulted in multiple births. (Source: Morbidity and Mortality Weekly Report)
a. Find the probability that a randomly selected infant was conceived through ART and was part of a multiple birth.
Textbook Question
2. Determine whether each number could represent the probability of an event. Explain your reasoning. b. 333.3%