Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

10. Combinatorics & Probability

Probability

College Algebra

10. Combinatorics & Probability

Probability

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1:56 minutes

Problem 11

Textbook Question

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

Verified step by step guidance

Understand that a standard die has 6 faces, each with a unique number from 1 to 6.

Identify that the event of interest is rolling a 4.

Recognize that there is only one face with the number 4 on a standard die.

Calculate the probability of rolling a 4 by dividing the number of favorable outcomes (rolling a 4) by the total number of possible outcomes (rolling any number from 1 to 6).

Express the probability as a fraction: \( \frac{1}{6} \).

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Key Concepts

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

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. An event with a probability of 0 means it cannot happen, while a probability of 1 means it is certain to happen. In this context, we are interested in the probability of rolling a specific number on a die.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For a single roll of a fair six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which specific events are measured.

Favorable Outcomes

Favorable outcomes refer to the specific results of an experiment that satisfy the condition of interest. In this case, the favorable outcome is rolling a 4. To find the probability of this event, we compare the number of favorable outcomes to the total number of outcomes in the sample space.