Skip to main content
Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 39
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 guidance
1
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

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.
Recommended video:
5:37
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.
Recommended video:
4:04
Fundamental Counting Principle

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.
Recommended video:
5:37
Introduction to Probability
Related Practice
Textbook Question

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

595
views
Textbook Question

Find each indicated sum. ∑i=04(−1)ii!\(\sum\)_{i=0}^{4} \(\frac{(-1)^i}{i!}\)

860
views
Textbook Question

Find the term indicated in each expansion. (2x + y)6; third term

599
views
Textbook Question

Find the sum of each infinite geometric series. 3 + 3/4 + 3/42 + 3/43 + ...

862
views
Textbook Question

Find the sum of the first 60 positive even integers.

1275
views
Textbook Question

Find the term indicated in each expansion. (x − 1)9; fifth term

627
views