In Exercises 11–16, a die is rolled. Find the probability of getting a 4.

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Step 1: Understand the problem context. A standard die has 6 faces, numbered from 1 to 6, and each face is equally likely to appear when rolled.

Step 2: Identify the total number of possible outcomes. Since the die has 6 faces, the total number of outcomes is \(6\).

Step 3: Determine the number of favorable outcomes. We want the probability of rolling a 4, so there is only 1 favorable outcome (the face showing 4).

Step 4: Use the probability formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).

Step 5: Substitute the values into the formula: \(\text{Probability of getting a 4} = \frac{1}{6}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sample Space

The sample space is the set of all possible outcomes of an experiment. For a single roll of a standard die, the sample space consists of six outcomes: {1, 2, 3, 4, 5, 6}. Understanding the sample space is essential to calculate probabilities accurately.

Event

An event is a specific outcome or a set of outcomes from the sample space. In this question, the event is rolling a 4, which is a single outcome within the sample space. Identifying the event helps in determining the favorable outcomes.

Probability Calculation

Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. For rolling a 4 on a die, the probability is 1 favorable outcome divided by 6 total outcomes, resulting in a probability of 1/6.

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