Textbook Question
Use the formula for nCr to evaluate each expression. 7C7
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 13
In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.
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Identify the total number of possible outcomes when rolling a die. Since a standard die has 6 faces, the total number of outcomes is 6.
Determine the favorable outcomes for the event. The event is getting an odd number, so list the odd numbers on a die: 1, 3, and 5.
Count the number of favorable outcomes. There are 3 odd numbers on the die.
Use the probability formula: \(P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\).
Substitute the values into the formula: \(P(\text{odd number}) = \frac{3}{6}\). This fraction can be simplified if needed.
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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 die roll, the sample space consists of the numbers 1 through 6, representing each face of the die.
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Event
An event is a subset of the sample space that includes outcomes of interest. In this case, the event is rolling an odd number, which includes the outcomes {1, 3, 5}.
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Probability Calculation
Probability is calculated as the ratio of favorable outcomes to total possible outcomes. For rolling an odd number, it is the number of odd outcomes divided by the total outcomes, i.e., 3/6 or 1/2.
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Related Practice
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Use the Binomial Theorem to expand each binomial and express the result in simplified form.
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Textbook Question
Use the Binomial Theorem to expand each binomial and express the result in simplified form.