Textbook Question
Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.
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 39
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.
Verified step by step guidance1
Identify the total number of possible outcomes, which is the total number of cards in the deck. Since there are 52 cards, the total number of outcomes is \(52\).
Determine the number of favorable outcomes for the event 'not dealt a king.' Since there are 4 kings in the deck, the number of cards that are not kings is \(52 - 4 = 48\).
Recall that the probability of an event is given by the formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).
Substitute the values into the formula: \(\text{Probability(not dealt a king)} = \frac{48}{52}\).
Simplify the fraction if possible to express the probability in simplest form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Basic Probability
Probability measures the likelihood of an event occurring, calculated as the ratio of favorable outcomes to total possible outcomes. In this problem, it involves finding the chance of not drawing a king from a deck.
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Introduction to Probability
Counting Outcomes in a Deck of Cards
A standard deck has 52 cards with 4 kings. Understanding the total number of cards and how many are kings is essential to determine favorable and unfavorable outcomes.
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Complement Rule in Probability
The complement rule states that the probability of an event not happening equals one minus the probability that it does happen. Here, finding the probability of not getting a king is easier by subtracting the probability of getting a king from 1.
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5:37Introduction to Probability
Related Practice
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