/*! 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 2 College Degrees. Of all postseco... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 2

College Degrees. Of all postsecondary degrees awarded in the United States, including master's and doctorate degrees, \(21 \%\) are associate's degrees, \(58 \%\) are earned by people whose race is White, and \(12 \%\) are associate's degrees earned by Whites. \(-\) Make a Venn diagram and use it to answer these questions. a. What percentage of all degrees are associate's degrees earned by non- Whites? b. What percentage of non-Whites earn a college degree other than an associate's degree? c. What percentage of all degrees are earned by nonWhites?

Short Answer

Expert verified
a) 9%, b) 33%, c) 42%

Step by step solution

01

Define Sets and Values

Define the sets: Let \( A \) be the set of all associate's degrees, and \( W \) be the set of all degrees earned by Whites. We know the following percentages: \( P(A) = 21\% \), \( P(W) = 58\% \), and \( P(A \cap W) = 12\% \).
02

Calculate Associate's Degrees by Non-Whites

To find the percentage of associate's degrees earned by non-Whites, calculate \( P(A) - P(A \cap W) = 21\% - 12\% = 9\% \).
03

Use Venn Diagram to Calculate Non-Associate Degrees by Non-Whites

The area outside both sets \( A \) and \( W \) on a Venn diagram represents degrees that are neither associate's nor earned by Whites. Find \( P(\text{other degrees by Non-Whites}) = P(W^c) - (P(A) - P(A \cap W)) = 42\% - 9\% = 33\% \), where \( P(W^c) = 100\% - P(W) = 42\% \).
04

Calculate All Degrees Earned by Non-Whites

Degrees by Non-Whites include those earned by non-associate degree holders and associate degree holders: \( P(W^c) = 100\% - P(W) = 42\% \).

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.

Set Theory
Set theory is a fundamental branch of mathematics that deals with the concept of sets, which are basically collections of objects. In this exercise, we're looking at sets in the context of Venn diagrams to visualize relationships between different groups. In particular, we have:
  • The set of all associate's degrees, denoted as \( A \).
  • The set of all degrees earned by Whites, denoted as \( W \).
Using the provided data, we can compute intersections and complements of these sets:

  • \( P(A) = 21\% \) represents the percentage of all degrees that are associate's degrees.
  • \( P(W) = 58\% \) shows the percentage of degrees earned by Whites.
  • \( P(A \cap W) = 12\% \) illustrates when both conditions are met, i.e., associate's degrees earned by Whites.
With these sets, you can easily visualize different groups using a Venn diagram, which aids in understanding complex relationships mathematically.
Associates Degree
Associate's degrees are significant as they represent a foundational level of postsecondary education. Typically, an associate's degree is an undergraduate degree awarded after a course of postsecondary study lasting two to three years.

This type of degree is often pursued for various practical reasons:
  • It is a quicker and more cost-effective way to enter the workforce.
  • Serves as a stepping stone if one plans to pursue a bachelor's degree later.
  • In several professional fields, an associate's degree is the minimum credential required to obtain a job.
In this exercise, we learn that \( 21\% \) of degrees are associate's degrees, revealing how vital these degrees are within the wider scope of postsecondary education in the United States.
Race Demographics
Race demographics play a crucial role in understanding educational statistics, as they highlight disparities and trends in educational attainment among different racial groups. In the current context, we know:
  • \( 58\% \) of degrees are earned by Whites.
  • \( 12\% \) of these degrees are associate's degrees earned by Whites.
From these statistics, we can deduce several insights:
  • The remaining \( 42\% \) of degrees are earned by non-Whites, stressing the diversity within higher education.
  • Understanding these demographics can help identify areas where educational opportunities may need to be improved or made more inclusive.
By analyzing such figures, stakeholders can develop policies that promote equitable educational opportunities across different racial and ethnic groups.
Postsecondary Education
Postsecondary education encompasses all types of education pursued after completing high school, including associate's, bachelor's, master's, and doctoral degrees. It plays a pivotal role in today's knowledge-driven society. Here's why it's important:
  • It provides individuals with the advanced skills and knowledge needed to succeed in various professional fields.
  • Contributes to personal development, critical thinking, and opens up broader career opportunities.
  • Data such as the percentage of associate's and other degrees earned provides insights into educational trends and workforce readiness.
In this exercise, we observe that associate's degrees are a significant component of the postsecondary landscape, making up \( 21\% \) of all degrees. This indicates their relevance and how they contribute to the collective credential pool in the U.S. education system.

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

Let \(A\) be the event that the student is enrolled in a four-year college and \(B\) the event that the student is female. The proportion of females enrolled in a four-year college is expressed in probability notation as a. \(P(A\) and \(B)\). b. \(P(A \mid B)\). c. \(P(B \mid A)\).

Playing the Lottery. New York State's "Quick Draw" lottery moves right along. Players choose between 1 and 10 numbers from the range 1 to \(80 ; 20\) winning numbers are displayed on a screen every four minutes. If you choose just one number, your probability of winning is \(20 / 80\), or \(0.25\). Lester plays one number eight times as he sits in a bar. What is the probability that all eight bets lose?

The Probability of a Flush. A poker player holds a flush when all five cards in the hand belong to the same suit (clubs, diamonds, hearts, or spades). We will find the probability of a flush when five cards are drawn in succession from the top of the deck. Remember that a deck contains 52 cards, 13 of each suit, and that when the deck is well shuffled, each card drawn is equally likely to be any of those that remain in the deck. a. Concentrate on spades. What is the probability that the first card drawn is a spade? What is the conditional probability that the second card drawn is a spade, given that the first is a spade? (Hint: How many cards remain? How many of these are spades?) b. Continue to count the remaining cards to find the conditional probabilities of a spade for the third, the fourth, and the fifth card drawn, given in each case that all previous cards are spades. c. The probability of drawing five spades in succession from the top of the deck is the product of the five probabilities you have found. Why? What is this probability? d. The probability of drawing five hearts or five diamonds or five clubs is the same as the probability of drawing five spades. What is the probability that the five cards drawn all belong to the same suit?

Universal Blood Donors. People with type O-negative blood are referred to as universal donors, although if you give type O-negative blood to any patient, you run the risk of a transfusion reaction due to certain antibodies present in the blood. However, any patient can receive a transfusion of O-negative red blood cells. Only 7.2\% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor?

White Cats and Deafness. Although cats generally possess an acute sense of hearing, due to an anomaly in their genetic makeup, deafness among white cats with blue eyes is quite common. Approximately \(95 \%\) of the general cat population are non-white cats (i.e., not pure white), and congenital deafness is extremely rare in non-white cats. However, among white cats, approximately \(75 \%\) with two blue eyes are deaf, \(40 \%\) with one blue eye are deaf, and only \(19 \%\) with eyes of other colors are deaf. In addition, among white cats, approximately \(23 \%\) have two blue eyes, \(4 \%\) have one blue eye, and the remainder have eyes of other colors. 10 a. Draw a tree diagram for selecting a white cat (outcomes: one blue eye, two blue eyes, or eyes of other colors) and deafness (outcomes: deaf or not deaf). b. What is the probability that a randomly chosen white cat is deaf?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.