Skip to main content
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 3.4.44b
Capitolo 3, Problema 3.4.44b

Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team.
b. What is the probability that none of the offices are filled by members of the debate team?

Guida verificata passo dopo passo
1
Step 1: Understand the problem. We are tasked with finding the probability that none of the four offices (president, vice president, secretary, and treasurer) are filled by members of the debate team. There are 14 candidates in total, 6 of whom are members of the debate team, leaving 8 candidates who are not members of the debate team.
Step 2: Calculate the total number of ways to assign the four offices. Since the order of selection matters (e.g., president is different from vice president), this is a permutation problem. The total number of permutations is given by the formula: P(14,4)=14!(14-4)!.
Step 3: Calculate the number of favorable outcomes where none of the offices are filled by members of the debate team. Since there are 8 candidates who are not members of the debate team, we calculate the number of permutations of 4 offices from these 8 candidates using the formula: P(8,4)=8!(8-4)!.
Step 4: Compute the probability that none of the offices are filled by members of the debate team. The probability is the ratio of the number of favorable outcomes to the total number of outcomes: P=P(8,4)P(14,4).
Step 5: Simplify the probability expression and interpret the result. This will give you the likelihood that none of the offices are filled by members of the debate team. Ensure you understand that this probability is based on the assumption that all candidates are equally likely to be chosen.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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 none of the selected candidates for the club offices are members of the debate team. Understanding how to compute probabilities is essential for solving the question.
Video consigliato:
Percorso guidato
5:37
Introduction to Probability

Combinatorics

Combinatorics is a branch of mathematics dealing with combinations and permutations of objects. In this scenario, it is crucial to determine how many ways the offices can be filled from the pool of candidates, specifically focusing on the selection of candidates who are not members of the debate team. This concept helps in calculating the total possible outcomes.

Complementary Events

Complementary events are pairs of outcomes where one event occurs if and only if the other does not. In this question, the event of interest is that none of the offices are filled by debate team members, which can be analyzed by considering the complementary event of at least one office being filled by a debate team member. This understanding aids in simplifying the probability calculations.
Video consigliato:
Percorso guidato
4:23
Complementary Events
Pratica correlata
Domanda del libro di testo

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.

b. The person is female or does not work from home.

" style="" width="400">

85
views
Domanda del libro di testo

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)

b. Find the probability that none of the four has lost a friend or relative to murder."

61
views
Domanda del libro di testo

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

b. Find the probability that neither probable voter would like entertainers to address social and political issues."

63
views
Domanda del libro di testo

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

b. Randomly selecting a person from the sample who is conservative or very conservative

91
views
Domanda del libro di testo

Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

8. Retirement Savings The table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at

work.

b. Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work.

125
views
Domanda del libro di testo

2. Determine whether each number could represent the probability of an event. Explain your reasoning. b. 333.3%

161
views