Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 3 - Probability

Problem 3.Q.2e

Chapter 3, Problem 3.Q.2e

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 obtained a bachelor's degree in natural sciences/mathematics.

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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 refers to the chance of randomly selecting a person who earned a bachelor's degree in natural sciences/mathematics from the total number of degrees conferred. Understanding how to calculate probability is essential for answering the question accurately.

Total Counts

Total counts refer to the sum of all occurrences of a particular category within a dataset. In the table, the total number of degrees conferred in each field and level of degree is crucial for determining the overall probability. For instance, the total number of bachelor's degrees is necessary to find the probability of selecting a bachelor's degree in natural sciences/mathematics.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. In this scenario, we are interested in the probability of selecting a bachelor's degree in natural sciences/mathematics, which is a specific condition within the broader context of all degrees. This concept helps in understanding how to narrow down the sample space when calculating probabilities.

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Related Practice

Textbook Question

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

51. A shipment of 200 calculators contains 3 defective units. What is the probability that a sample of three calculators will have

c. at least one defective calculator?

Textbook Question

"In Exercises 5 and 6, use the Fundamental Counting Principle.

5. A student must choose from seven classes to take at 8:00 A.M., four classes to take at 9:00 A.M., and three classes to take at 10:00 A.M. How many ways can the student arrange the schedule?"

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

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?