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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 3 - ProbabilityProblema 3.4.15
Capitolo 3, Problema 3.4.15

In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.
15. The number of ways 16 floats can line up in a row for a parade

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Identify the key elements of the problem: The problem involves arranging 16 floats in a specific order for a parade. This indicates that the order of arrangement is important.
Recall the definition of permutations: A permutation is used when the order of arrangement matters. The formula for permutations of n items is n! (n factorial), which represents the product of all positive integers from 1 to n.
Determine whether the problem involves permutations, combinations, or neither: Since the order of the floats in the parade matters, this situation involves permutations.
Write the formula for the number of permutations: The number of ways to arrange 16 floats in a row is given by 16! (16 factorial).
Explain the reasoning: The problem involves arranging all 16 floats in a specific order, and since order matters, it is a permutation problem. The solution is calculated using the factorial of 16.

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Permutations

Permutations refer to the arrangement of items in a specific order. When the order of selection matters, such as lining up floats for a parade, we use permutations. The formula for permutations of 'n' items taken 'r' at a time is n! / (n - r)!, where '!' denotes factorial, the product of all positive integers up to 'n'.
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Introduction to Permutations

Combinations

Combinations involve selecting items without regard to the order of selection. This concept is used when the arrangement does not matter, such as choosing a committee from a group. The formula for combinations of 'n' items taken 'r' at a time is n! / [r!(n - r)!], highlighting that the order of selection is irrelevant.
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Combinations

Factorial

Factorial, denoted as 'n!', is a mathematical operation that multiplies a number by all positive integers less than it. It is fundamental in both permutations and combinations, as it helps calculate the total arrangements or selections of items. For example, 5! equals 5 × 4 × 3 × 2 × 1 = 120, which is crucial for determining the number of ways to arrange or select items.
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Combinations
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Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.

28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

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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.

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31. Experiment A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment. In how many different ways can the treatment group be selected?

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Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)

49. 18 to 24 years old

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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

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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.

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