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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 3.2.25b
Capitolo 3, Problema 3.2.25b

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.
(Adapted from YouGov)
b. Find the probability that neither adult U.S. citizen says that Barack Obama was the best president in U.S. history."

Guida verificata passo dopo passo
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Step 1: Understand the problem. We are tasked with finding the probability that neither of the two randomly selected adult U.S. citizens believes Barack Obama was the best president in U.S. history. This involves using the Multiplication Rule for probabilities.
Step 2: Calculate the probability that a single adult U.S. citizen does not believe Barack Obama was the best president. From the sample, 270 out of 1500 said he was the best president. Therefore, the probability that a single person does not believe this is given by \( P(\text{not Obama}) = 1 - \frac{270}{1500} \).
Step 3: Recognize that the two selections are made without replacement. This means the probability for the second selection depends on the outcome of the first selection. For the first selection, the probability that the person does not believe Barack Obama was the best president is \( P(\text{not Obama}) \).
Step 4: For the second selection, if the first person selected does not believe Barack Obama was the best president, the total number of people who do not believe this decreases by 1, and the total population decreases by 1. Thus, the probability for the second selection is \( P(\text{not Obama on second draw}) = \frac{N_{\text{not Obama}} - 1}{1500 - 1} \), where \( N_{\text{not Obama}} \) is the number of people who do not believe Barack Obama was the best president.
Step 5: Apply the Multiplication Rule. The probability that neither of the two selected individuals believes Barack Obama was the best president is the product of the probabilities for the first and second selections: \( P(\text{neither}) = P(\text{not Obama on first draw}) \times P(\text{not Obama on second draw}) \). Substitute the values from the previous steps to compute the final probability.

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Multiplication Rule

The Multiplication Rule in probability states that the probability of two independent events both occurring is the product of their individual probabilities. In this context, it helps calculate the likelihood of multiple selections from a population, where the outcome of one selection does not affect the other.
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Percorso guidato
05:17
Multiplication Rule: Dependent Events

Probability of an Event

Probability quantifies the likelihood of an event occurring, expressed as a number between 0 and 1. In this scenario, we need to determine the probability that a randomly selected adult does not believe Barack Obama was the best president, which involves calculating the complement of the probability that they do.
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Percorso guidato
05:54
Probability of Multiple Independent Events

Complement Rule

The Complement Rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. For this question, if we know the probability of an adult saying Obama is the best president, we can easily find the probability that neither of the two selected adults holds that opinion by applying this rule.
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Percorso guidato
03:53
Conditional Probability Rule
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.

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Domanda del libro di testo

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

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

b. Find the probability that none of the six have type O+ blood."

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Domanda del libro di testo

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

25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.

(Adapted from YouGov)

c. Find the probability that at least one of the two adult U.S. citizens says that Barack Obama was the best president in U.S. history."

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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

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

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88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is between \$21 and \$50.

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