Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 3 - Probability

Problem 3.2.7b

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 guidance

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.

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.

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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b. Rolling a 2 or an odd number

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a. Find the probability that all four have lost a friend or relative to murder.

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(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."

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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.

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Textbook Question

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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.

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Textbook Question

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

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