Domanda del libro di testo
Use mathematical induction to prove that each statement is true for every positive integer n. 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)
645
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 15
In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.
Guida verificata passo dopo passo1
Identify the total number of possible outcomes when rolling a standard die. Since a die has 6 faces, the total number of outcomes is \(6\).
Determine the favorable outcomes for the event "getting a number greater than 4." The numbers greater than 4 on a die are \(5\) and \(6\).
Count the number of favorable outcomes. There are \(2\) such numbers: \(5\) and \(6\).
Use the probability formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).
Substitute the values into the formula: \(\text{Probability} = \frac{2}{6}\). This fraction can be simplified if needed.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
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 the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is essential to determine the total number of possible outcomes.
Video consigliato:
5:37
Introduction to Probability
Event
An event is a subset of the sample space that includes outcomes of interest. In this problem, the event is rolling a number greater than 4, which includes the outcomes {5, 6}. Identifying the event helps in calculating the probability.
Video consigliato:
4:23Complementary Events
Probability Calculation
Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. Here, the probability of rolling a number greater than 4 is the number of favorable outcomes (2) divided by the total outcomes (6), resulting in 2/6 or 1/3.
Video consigliato:
5:37Introduction to Probability
Pratica correlata
Domanda del libro di testo
Use the Binomial Theorem to expand each binomial and express the result in simplified form.
717
views
Domanda del libro di testo
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a1 = 13, d = 4.
919
views
Domanda del libro di testo
Use the formula for nCr to evaluate each expression. 5C0
758
views
2
rank
Domanda del libro di testo
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a1=3 and an=4an-1 for n≥2
953
views
Domanda del libro di testo
Use the formula for nCr to evaluate each expression. 4C4
58
views