Domanda del libro di testo
Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence whose nth term is an = (3)5n Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 9, Problema 89
A die is rolled. Find the probability of getting a number less than 5.
Guida verificata passo dopo passo1
Step 1: Understand the problem. A standard die has 6 faces numbered 1 through 6. The goal is to find the probability of rolling a number less than 5.
Step 2: Identify the favorable outcomes. Numbers less than 5 on a die are 1, 2, 3, and 4. This gives us 4 favorable outcomes.
Step 3: Determine the total possible outcomes. Since a die has 6 faces, there are 6 possible outcomes in total.
Step 4: Use the probability formula: \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Substitute the values: \( P(E) = \frac{4}{6} \).
Step 5: Simplify the fraction if necessary. \( \frac{4}{6} \) can be simplified to \( \frac{2}{3} \). This represents the probability of rolling a number less than 5.
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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 will not happen, while a probability of 1 means it will certainly happen. In this context, we are interested in the probability of rolling a number less than 5 on a standard six-sided die.
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5:37
Introduction to Probability
Sample Space
The sample space is the set of all possible outcomes of a random experiment. For a single roll of a 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 can be measured.
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5:37Introduction to Probability
Favorable Outcomes
Favorable outcomes refer to the specific outcomes in the sample space that satisfy the condition of the event we are interested in. In this case, the favorable outcomes for rolling a number less than 5 are {1, 2, 3, 4}, which totals four outcomes. The probability of the event is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space.
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4:23Complementary Events
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