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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 3.1.46
Capitolo 3, Problema 3.1.46

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.
46. Event F: rolling a number divisible by 5

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Step 1: Understand the problem. The experiment involves rolling a 12-sided die numbered from 1 to 12. The goal is to find the probability of rolling a number divisible by 5.
Step 2: Identify the numbers divisible by 5 within the range of 1 to 12. A number is divisible by 5 if it can be expressed as 5 × k, where k is an integer. In this case, the numbers divisible by 5 are 5 and 10.
Step 3: Count the total number of outcomes in the sample space. Since the die has 12 sides, the total number of outcomes is 12.
Step 4: Count the favorable outcomes for Event F. The favorable outcomes are the numbers divisible by 5, which are 5 and 10. Therefore, there are 2 favorable outcomes.
Step 5: Calculate the probability using the classical probability formula: \( P(F) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Substitute the values: \( P(F) = \frac{2}{12} \). Simplify the fraction if needed.

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Classical Probability

Classical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in a probability experiment. It assumes that all outcomes are equally likely. For example, when rolling a 12-sided die, the total outcomes are 12, and the probability of rolling a specific number is 1/12.
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Introduction to Probability

Divisibility

Divisibility is a mathematical concept that determines whether one integer can be divided by another without leaving a remainder. In the context of the given problem, we are interested in the numbers on the die that are divisible by 5, which are 5 and 10. Understanding which numbers meet this criterion is essential for calculating the probability of event F.
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Difference in Means: Hypothesis Tests Example 1

Event and Sample Space

An event is a specific outcome or a set of outcomes from a probability experiment, while the sample space is the set of all possible outcomes. In this case, the sample space consists of the numbers 1 through 12 on the die, and event F includes the outcomes that are divisible by 5. Identifying the event and sample space is crucial for calculating the probability of event F.
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Sampling Distribution of Sample Proportion
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