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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 3.2.24a
Capitolo 3, Problema 3.2.24a

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)
a. Find the probability that all four have lost a friend or relative to murder.

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Step 1: Understand the problem. We are tasked with finding the probability that all four randomly selected children have lost a friend or relative to murder. This involves using the Multiplication Rule for independent events, as the probability of one child being affected does not influence the others.
Step 2: Identify the given information. From the problem, we know that 8% of children (or 0.08 as a decimal) have lost a friend or relative to murder. This is the probability of a single child being affected, denoted as P(A) = 0.08.
Step 3: Recognize that the events are independent. Since the selection of one child does not affect the selection of another, the probability of all four children being affected can be calculated by multiplying the probabilities of each child being affected.
Step 4: Apply the Multiplication Rule. The probability of all four children being affected is given by the formula: P(All 4) = P(A) × P(A) × P(A) × P(A), which can also be written as P(All 4) = P(A)^4.
Step 5: Substitute the given probability into the formula. Replace P(A) with 0.08 in the formula P(All 4) = P(A)^4 to calculate the probability. This will give you the final result.

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Multiplication Rule of Probability

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this context, if the events are the selection of children who have lost a friend or relative to murder, the rule allows us to calculate the probability of all selected children experiencing this event by multiplying the individual probabilities for each child.
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Probability of Multiple Independent Events

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the selection of one child does not influence the selection of another, assuming the sample size is large enough. This independence is crucial for applying the Multiplication Rule correctly, as it ensures that the probabilities can be multiplied without adjustment.
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Probability of Multiple Independent Events

Probability Calculation

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. To find the probability that all four selected children have lost a friend or relative to murder, we first determine the probability for one child (8% or 0.08) and then raise this probability to the power of four, reflecting the four independent selections.
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Probability From Given Z-Scores - TI-84 (CE) Calculator
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