Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook

Larson 8th Edition

Ch. 3 - Probability

Problem 3.Q.2h

Chapter 3, Problem 3.Q.2h

The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)
A person who earned a degree in the year is randomly selected. Find the probability that the degree earned by the person is a
g. bachelor's degree and the degree is in natural sciences/mathematics.

Verified step by step guidance

Step 1: Identify the relevant data from the table. The number of bachelor's degrees in natural sciences/mathematics is 175.5 (in thousands), and the total number of degrees conferred across all fields and levels is 565.4 (in thousands).

Step 2: Recall the formula for probability. The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the favorable outcome is earning a bachelor's degree in natural sciences/mathematics.

Step 3: Write the probability formula for this scenario: \( P = \frac{\text{Number of bachelor's degrees in natural sciences/mathematics}}{\text{Total number of degrees}} \). Using MathML, this can be expressed as:

P = \frac{175.5}{565.4}

Step 4: Simplify the fraction to calculate the probability. This involves dividing the numerator (175.5) by the denominator (565.4).

Step 5: Interpret the result. The probability represents the likelihood that a randomly selected person who earned a degree in the year earned a bachelor's degree in natural sciences/mathematics.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

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 involves calculating the chance that a randomly selected degree is a bachelor's degree in natural sciences/mathematics. This is determined by dividing the number of bachelor's degrees in that field by the total number of degrees conferred.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this scenario, it helps in understanding how the selection of a degree type (bachelor's) influences the probability of it being in a specific field (natural sciences/mathematics). This concept is crucial for interpreting the results accurately.

Data Interpretation

Data interpretation involves analyzing and making sense of data presented in tables or graphs. In this case, it requires extracting relevant figures from the provided table to compute the desired probability. Understanding how to read and interpret the data accurately is essential for solving the problem effectively.

Recommended video:

4:01

Introduction to Collecting Data

Related Practice

Textbook Question

The table shows the results of a survey in which 3,545,286 public and 509,168 private school teachers were asked about their full-time teaching experience.

Are the events “being a public school teacher” and “having more than 20 years of full-time teaching experience” independent? Explain.

Textbook Question

6. A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive

c. at least one good unit.

Textbook Question

4. Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning.

Event A: A bowler having the highest game in a 40-game tournament

Event B: Losing the bowling tournament

Textbook Question

The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)

A person who earned a degree in the year is randomly selected. Find the probability that the degree earned by the person is a

a. bachelor's degree.

Textbook Question

The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)

A person who earned a degree in the year is randomly selected. Find the probability that the degree earned by the person is a

g. bachelor's degree and the degree is in natural sciences/mathematics.

Textbook Question

In Exercises 49-53, use counting principles to find the probability.

53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the

probability of choosing

c. two men and two women?