/*! 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 15 According to the U.S. Census Bur... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 15

According to the U.S. Census Bureau, \(8.0 \%\) of 16 - to 24 -year-olds are high school dropouts. In addition, \(2.1 \%\) of 16 - to 24 -year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16 - to 24 -year-old is unemployed, given he or she is a dropout?

Short Answer

Expert verified
The probability is 0.2625 or 26.25%.

Step by step solution

01

Understand the given probabilities

Identify the given probabilities in the problem. The probability that a 16 - to 24-year-old is a high school dropout is given as: \(P(D) = 0.08\), and the probability that a 16 - to 24-year-old is both a high school dropout and unemployed is: \(P(D \text{ and } U) = 0.021\).
02

Apply the conditional probability formula

Recall the formula for conditional probability: \(P(A | B) = \frac{P(A \text{ and } B)}{P(B)}\). Here, we need to find the probability that a 16 - to 24-year-old is unemployed, given that they are a high school dropout. Therefore, we use \(P(U | D) = \frac{P(U \text{ and } D)}{P(D)}\).
03

Substitute the values into the formula

Substitute the given probabilities into the conditional probability formula: \(P(U | D) = \frac{0.021}{0.08}\).
04

Simplify the expression

Calculate the result of the division: \(P(U | D) = \frac{0.021}{0.08} = 0.2625\). Therefore, the probability that a randomly selected 16 - to 24-year-old is unemployed given that he or she is a dropout is 0.2625 or 26.25\%.

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.

Probability
Probability is a measure of the likelihood that an event will occur. It ranges from 0 (impossibility) to 1 (certainty). For example, the chance of getting heads when flipping a fair coin is 0.5 or 50%.
To solve the given exercise, we used conditional probability. This concept helps us find the likelihood of an event happening based on the condition that another event has already occurred.
The formula for conditional probability is: \(P(A | B) = \frac{P(A \text{ and } B)}{P(B)}\).
Using this, we calculated the probability that a 16 to 24-year-old is unemployed, given that they are a high school dropout. We substituted the given values and found that the probability is 26.25%.
High School Dropouts
High school dropouts refer to individuals who do not complete their high school education. According to the U.S. Census Bureau, 8.0% of 16 to 24-year-olds fall into this category.
Dropping out of high school can have significant long-term impacts, including lower income, higher likelihood of unemployment, and fewer career opportunities.
In the context of the exercise, we used the probability of being a high school dropout, labeled as \(P(D) = 0.08\). This was crucial in calculating the conditional probability of being unemployed given dropout status.
U.S. Census Bureau
The U.S. Census Bureau is the government agency responsible for collecting and providing data about the people and economy of the United States. They conduct various surveys and censuses to gather information about different aspects of society.
For our exercise, the U.S. Census Bureau provided the statistics that 8.0% of 16 to 24-year-olds are high school dropouts, and 2.1% are both dropouts and unemployed.
Reliable data from sources like the U.S. Census Bureau helps in performing accurate probability calculations and making informed decisions based on those probabilities.
Unemployment Rate
The unemployment rate is the percentage of people in the labor force who are jobless and actively seeking work.
In our problem, we focused on the unemployment rate among high school dropouts aged 16 to 24.
We found that 2.1% of this age group are both high school dropouts and unemployed, given as \(P(D \text{ and } U) = 0.021\).
Understanding the unemployment rate is important, as it reflects the health of the economy and can influence policy decisions and educational programs aimed at reducing dropout rates and improving job prospects.

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 combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed.

According to a Gallup Poll, about \(17 \%\) of adult Americans bet on professional sports. Census data indicate that \(48.4 \%\) of the adult population in the United States is male. (a) Assuming that betting is independent of gender, compute the probability that an American adult selected at random is male and bets on professional sports. (b) Using the result in part (a), compute the probability that an American adult selected at random is male or bets on professional sports. (c) The Gallup poll data indicated that \(10.6 \%\) of adults in the United States are males and bet on professional sports. What does this indicate about the assumption in part (a)? (d) How will the information in part (c) affect the probability you computed in part (b)?

How many different license plate numbers can be made by using one letter followed by five digits selected from the digits 0 through 9?

Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a) Compute the probability that 10 people have 10 different birthdays. Hint: The first person's birthday can occur 365 ways, the second person's birthday can occur 364 ways, because he or she cannot have the same birthday as the first person, the third person's birthday can occur 363 ways, because he or she cannot have the same birthday as the first or second person, and so on. (b) The complement of "10 people have different birthdays" is "at least 2 share a birthday." Use this information to compute the probability that at least 2 people out of 10 share the same birthday.

According to Internal Revenue Service records, \(6.42 \%\) of all household tax returns are audited. According to the Humane Society, \(39 \%\) of all households own a dog. Assuming dog ownership and audits are independent events, what is the probability a randomly selected household is audited and owns a dog?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.