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 3.2.7b
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.
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the conditional probability that a randomly selected bachelor's degree-earning student received a business degree, given that the student is female. Conditional probability is calculated using the formula P(A|B) = P(A ∩ B) / P(B), where A is the event of receiving a business degree and B is the event of being female.
Step 2: Identify the relevant values from the table. From the table, the number of female students who received business degrees is 181,362, and the total number of female students is 1,135,684.
Step 3: Calculate the numerator of the conditional probability formula, P(A ∩ B). This is the number of female students who received business degrees, which is 181,362.
Step 4: Calculate the denominator of the conditional probability formula, P(B). This is the total number of female students, which is 1,135,684.
Step 5: Divide the numerator by the denominator to find the conditional probability. The formula is P(A|B) = 181,362 / 1,135,684. Simplify the fraction to express the probability.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Conditional Probability
Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads as the probability of event A occurring given that event B has occurred. This concept is crucial for understanding how probabilities can change based on additional information, such as knowing the gender of a student when determining the probability of them having a business degree.
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Conditional Probability Rule
Joint Probability
Joint probability is the probability of two events occurring simultaneously. In the context of the given question, it involves calculating the probability of a student being both female and having received a business degree. This concept is essential for understanding how to derive conditional probabilities from a dataset, as it helps in identifying the intersection of the two events being analyzed.
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Marginal Probability
Marginal probability is the probability of a single event occurring without consideration of other events. It is calculated by summing the joint probabilities of the event across all possible outcomes. In this case, the marginal probability of a student being female can be found by summing the total number of female students, which is necessary for calculating the conditional probability of interest.
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5:37Introduction to Probability
Related Practice
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)
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."
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.
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.
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%