/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 In a deck of cards there are 12 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 27

In a deck of cards there are 12 face cards and 40 cards with numbers. What is the probability of selecting a face card from the deck?

Short Answer

Expert verified
The probability of selecting a face card from the deck is \( \frac{3}{13} \).

Step by step solution

01

- Understand the Problem

A standard deck of cards consists of 52 cards: 12 face cards (kings, queens, and jacks) and 40 cards with numbers (2 through 10). The task is to find the probability of drawing a face card.
02

- Calculate the Total Number of Outcomes

The total number of cards in the deck is 52. This represents all the possible outcomes when drawing a single card from the deck.
03

- Determine the Number of Favorable Outcomes

The number of face cards, which are the favorable outcomes, is 12.
04

- Set Up the Probability Formula

The probability of an event is given by the formula: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
05

- Insert Values into the Formula

Substitute the number of face cards (favorable outcomes) and the total number of cards into the formula: \[ P(\text{face card}) = \frac{12}{52} \]
06

- Simplify the Fraction

Simplify the fraction \( \frac{12}{52} \): \[ P(\text{face card}) = \frac{3}{13} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

standard deck of cards
A standard deck of cards is the foundation of many probability problems. It consists of 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades.
Each suit has 13 cards, including numbers and face cards.
Understanding the composition of a standard deck of cards is crucial for tackling various probability exercises.
face cards
In a standard deck, there are face cards in each suit. The face cards are the King, Queen, and Jack.
Therefore, with four suits and three face cards in each suit, the total number of face cards is 12.
These face cards are commonly involved in probability calculations.
simplifying fractions
Simplifying fractions makes it easier to understand and compare probabilities. When you have a fraction like \( \frac{12}{52} \), you can simplify it by finding a common factor for the numerator and the denominator.
In this case, both 12 and 52 can be divided by 4:
\[ \frac{12}{52} = \frac{12 \div 4}{52 \div 4} = \frac{3}{13} \]
This simplified fraction is easier to interpret in probability problems.
probability formula
The probability formula helps determine the likelihood of an event occurring. It is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
To find the probability of drawing a face card, we use this formula. We substitute the number of face cards (12) as the favorable outcomes and the total number of cards (52) as the total outcomes:
\[ P(\text{face card}) = \frac{12}{52} \]
After simplifying, we get the probability as \( \frac{3}{13} \). This means that the probability of drawing a face card is 3 out of 13.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A number of students at a large university were asked if they owned a car and if they lived in a dorm or off campus. The table shows the results. a. What is the probability that a student selected at random lives in a dorm? b. What is the probability that a student selected at random does not own a car? $$\begin{array}{|l|c|c|}\hline & \begin{array}{c}\text { Number of } \\\\\text { Car Owners }\end{array} & \begin{array}{c}\text { Number Who Do } \\\\\text { Not Own a Car }\end{array} \\\\\hline \text { Dorm resident } & 32 & 88 \\\\\hline \text { Lives off campus } & 59 & 26 \\\\\hline\end{array}$$

A jar contains 10 black marbles, 12 white marbles, and 4 blue marbles. What is the probability of selecting a blue marble or a black marble?

Use a protractor to construct an angle of the given measure. $$125^{\circ}$$

A card is chosen from a deck consisting of 10 cards numbered 1-10. Determine the sample space of this experiment.

The number of customer complaints for service representatives at a small company is given in the table. If one representative is picked at random, find the probability that the representative received a. Exactly 3 complaints b. Between 1 and 5 complaints, inclusive c. At least 4 complaints d. More than 5 complaints or fewer than 2 complaints $$\begin{array}{c|c}\begin{array}{c}\text { Number of } \\\\\text { Complaints }\end{array} & \begin{array}{c}\text { Number of } \\\\\text { Representatives }\end{array} \\\\\hline 0 & 4 \\\\\hline 1 & 2 \\\\\hline 2 & 14 \\\\\hline 3 & 10 \\\\\hline 4 & 16 \\\\\hline 5 & 18 \\\\\hline 6 & 10 \\\\\hline 7 & 6 \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.