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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.Q.6c
Chapter 3, Problem 3.Q.6c

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.

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Step 1: Understand the problem. We are tasked with finding the number of ways to select 3 units from a shipment of 250 netbooks, where at least one of the selected units is not defective. This means we need to exclude the cases where all 3 selected units are defective.
Step 2: Calculate the total number of ways to select 3 units from the shipment. Use the combination formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of items (250) and r is the number of items to choose (3). This gives us C(250, 3).
Step 3: Calculate the number of ways to select 3 defective units. Since there are only 3 defective units in the shipment, the number of ways to select all 3 defective units is C(3, 3).
Step 4: Subtract the number of ways to select all defective units from the total number of ways to select 3 units. This ensures that at least one of the selected units is not defective. The formula is: Total ways - Ways to select all defective units = C(250, 3) - C(3, 3).
Step 5: Simplify the expressions for C(250, 3) and C(3, 3) using the combination formula, but do not compute the final values. This will give you the number of ways to select 3 units with at least one good unit.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Combinatorics

Combinatorics is a branch of mathematics dealing with combinations and permutations of objects. In this context, it helps determine the number of ways to select units from a larger set, which is essential for calculating the different combinations of defective and non-defective netbooks.

Complementary Counting

Complementary counting is a technique used to simplify counting problems by calculating the total number of outcomes and subtracting the number of undesired outcomes. Here, it can be applied to find the number of ways to select three units that include at least one good unit by first calculating the total combinations and then subtracting the combinations that consist only of defective units.
Recommended video:
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Fundamental Counting Principle

Probability

Probability is the measure of the likelihood that an event will occur, often expressed as a fraction or percentage. In this scenario, understanding the probability of selecting at least one good unit from the shipment is crucial for evaluating the effectiveness of the vending company's purchase strategy.
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Introduction to Probability
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?

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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

134
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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.

84
views
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.

103
views
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.

68
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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?

204
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