/*! 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 7 An experiment consists of select... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 7

An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event. A king of diamonds is drawn.

Short Answer

Expert verified
The probability of drawing a King of Diamonds from a 52-card deck is \(P(\text{King of Diamonds}) = \frac{1}{52}\).

Step by step solution

01

Identify the total number of possible outcomes

We have a standard 52-card deck, so there are 52 possible cards that could be drawn.
02

Identify the successful outcomes

Only one card in the deck is a King of Diamonds, so there is only 1 successful outcome.
03

Calculate the probability

Now, divide the number of successful outcomes (1) by the total number of possible outcomes (52): \(P(\text{King of Diamonds}) = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{52}\)
04

Simplify the probability

The probability of drawing a King of Diamonds from a 52-card deck is: \(P(\text{King of Diamonds}) = \frac{1}{52}\)

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.

Combinatorics
Combinatorics is a branch of mathematics that deals with counting, arranging, and finding patterns. It is incredibly useful for calculating probabilities, especially in situations involving numerous possibilities and outcomes. In our exercise, combinatorics is at play when we deal with the deck's 52 possible cards.
  • Combinatorics helps us identify successful outcomes; in this case, only one card satisfies our condition鈥攖he King of Diamonds.
  • When calculating probabilities, we often use combinations and permutations, which are core principles of combinatorics.
Understanding these basics allows us to assess the chance of specific events happening, such as finding the likelihood of drawing particular cards from a deck. We count the number of favorable outcomes against the total possible number, crafting the foundation for probability calculations.
Statistics
Statistics is all about gathering, analyzing, and interpreting data. In probability, statistics provide the tools we need to make sense of random events. Our exercise here is a straightforward demonstration of a probabilistic event analyzed with statistical methods.
  • In this scenario, selecting cards is a statistical experiment鈥攊t involves making observations and drawing conclusions based on data (the cards drawn).
  • The probability calculated demonstrates a simple statistical measure, offering predictions on how often events occur on average under controlled circumstances.
By breaking down this data, statistics helps us understand random phenomena, allowing us to make informed guesses about uncertain situations, like drawing a specific card from a deck.
Card Probability
Card probability is a specialized area of probability focused on events involving playing cards. Since a deck has a fixed number of cards, it's an excellent opportunity to learn probability basics. Let's explore this using the exercise.
  • Each card drawn from a standard deck is an independent random event since the outcome of one draw doesn't affect the others.
  • The probability of drawing the King of Diamonds, calculated as \(\frac{1}{52}\), illustrates how probabilities of individual cards are determined based on their total count.
Card probability lets us predict outcomes and understand the likelihood of drawing specific cards. This knowledge can be applied in games and real-life decisions, improving strategic thinking and decision-making skills.

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

Five hundred raffle tickets were sold. What is the probability that a person holding one ticket will win the first prize? What is the probability that he or she will not win the first prize?

In a survey conducted in 2007 of 1402 workers 18 yr and older regarding their opinion on retirement benefits, the following data were obtained: 827 said that it was better to have excellent retirement benefits with a lower-than-expected salary, 477 said that it was better to have a higher-than-expected salary with poor retirement benefits, 42 said "neither," and 56 said "not sure." If a worker in the survey is selected at random, what is the probability that he or she answered that it was better to have a. Excellent retirement benefits with a lower-than-expected salary? b. A higher-than-expected salary with poor retirement benefits?

A time study was conducted by the production manager of Vista Vision to determine the length of time in minutes required by an assembly worker to complete a certain task during the assembly of its Pulsar color television sets. a. Describe a sample space corresponding to this time study. b. Describe the event \(E\) that an assembly worker took 2 min or less to complete the task. c. Describe the event \(F\) that an assembly worker took more than 2 min to complete the task.

In a Los Angeles Times poll of 1936 California residents conducted in February 2004 , the following question was asked: Do you favor or oppose an amendment to the U.S. Constitution barring same-sex marriage? The following results were obtained: $$ \begin{array}{lccc} \hline \text { Opinion } & \text { Favor } & \text { Oppose } & \text { Don't know } \\ \hline \text { Respondents } & 910 & 891 & 135 \\ \hline \end{array} $$ Determine the empirical probability distribution associated with these data.

STAYING IN ToucH In a poll conducted in 2007, 2000 adults ages 18 yr and older were asked how frequently they are in touch with their parents by phone. The results of the poll are as follows: $$ \begin{array}{lccccc} \hline \text { Answer } & \text { Monthly } & \text { Weekly } & \text { Daily } & \text { Don't know } & \text { Less } \\ \hline \text { Respondents, \% } & 11 & 47 & 32 & 2 & 8 \\ \hline \end{array} $$ If a person who participated in the poll is selected at random, what is the probability that the person said he or she kept in touch with his or her parents a. Once a week? b. At least once a week?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.