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$$ \begin{array}{lccc} \hline \text { Highest education } & \text { Total population } & \text { In labor force } & \text { Employed } \\ \text { Didn't finish high } & 27,669 & 12,470 & 11,408 \\ \text { school } & & & \\ \begin{array}{c} \text { High school but no } \\ \text { college } \end{array} & 59,860 & 37,834 & 35,857 \\ \begin{array}{c} \text { Less than bachelor's } \\ \text { degree } \end{array} & 47,556 & 34,439 & 32,977 \\ \text { College graduate } & 51,582 & 40,390 & 39,293 \\ \hline \end{array} $$ Unemployment (5.3) If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he or she is in the labor force? Show your work.

Step by step solution

01

Understand the problem

We need to find the probability that a randomly chosen person who is a college graduate is in the labor force.

02

Identify the relevant data for College Graduates

From the table, for College Graduates: - Total population = 51,582 - In labor force = 40,390.

03

Define probability concept

The probability we want is the number of college graduates in the labor force divided by the total number of college graduates.

04

Calculate the probability

The probability that a college graduate is in the labor force is given by the formula: \( P = \frac{\text{Number in labor force}}{\text{Total population}} \) Plugging in the numbers, \( P = \frac{40,390}{51,582} \approx 0.783 \).

05

Conclusion

Therefore, the probability that a randomly chosen college graduate is in the labor force is approximately 0.783.

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Key Concepts

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

Unemployment

Unemployment is when people who can work and want to work cannot find a job. It is a common topic in economics and affects the individual and society. Unemployment happens for various reasons, such as:

• Economic downturns where businesses close or reduce hiring
• Technological changes replacing jobs
• Seasonal changes affecting industries like tourism or agriculture

To measure unemployment, economists look at people without a job but actively looking for one. This is known as the "unemployment rate". It gives insights into economic health. When calculating the unemployment rate, it's important to know the size of the labor force and how many are actually employed. In our example, unemployment impacts different groups based on education.

College Graduates

College graduates are individuals who have completed a course of study at a college or university. This group is often perceived to have higher earning potential and more job opportunities. However, college graduates can also face unemployment depending on the job market.
For example, in our dataset:

• Total college graduates: 51,582
• In the labor force: 40,390
• Employed: 39,293

This shows that most college graduates join the labor force and find jobs. The probability exercise focuses on understanding these numbers to assess their participation in the labor market. Understanding how many college graduates are employed helps in evaluating economic trends and education's value.

Labor Force

The labor force is a group of people who are willing and able to work. It includes both employed individuals and those unemployed but actively seeking work. Understanding the labor force helps in economic planning and labor market analysis.

• Employed: People who have jobs
• Unemployed: People who do not have jobs but are looking for work

The labor force excludes individuals not actively seeking employment, such as retirees or students. In the context of the problem, the labor force for college graduates is important. Out of 51,582 college graduates, 40,390 are in the labor force. This indicates a high level of participation.

Probability Calculation

Probability is the chance that a particular event will occur. In our exercise, we calculated the probability that a college graduate is part of the labor force. The formula used is:\[ P = \frac{\text{Number in labor force}}{\text{Total population}} \]Plugging in the values for college graduates gives:\[ P = \frac{40,390}{51,582} \approx 0.783 \]
This probability of 0.783 means there is a 78.3% chance a randomly selected college graduate is in the labor force. Calculating probabilities like this helps understand trends and make predictions based on existing data.