Q.71 - The Practice of Statistics for AP

Question

In the language of government statistics, you are “in the labor force” if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged $25$ years and over in a recent year. The table entries are counts in thousands of people. 

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

Answer

The probability is $0.7830$

Step 1: Given information

Given in the question that, In the language of government statistics, you are “in the labor force” if you are available for work and either working or actively  seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged $25$ years and over in a recent year. The table entries are counts in thousands of people.

We need to find the probability that a randomly chosen person $25$ years of age or older is a college graduate.

Step 2: Explanation

The probability can be calculated by dividing the number of favorable outcomes by the number of possible outcomes.

If $A$ and $B$ are two events, then the conditional probability that event $A$ occurs when event $B$ has already occurred is

$P(A\mid B)=\frac{P\left(A\text{ and }B\right)}{P\left(B\right)}$

probability can be calculated by dividing the number of favorable outcomes by the number of possible outcomes.

Now, the probability that he or she is in the labor force and a college graduate is,

$\frac{40390}{27669+59860+47556+51582}=\frac{40390}{186667}$

The probability that he or she is a college graduate is,

$\frac{51582}{27669+59860+47556+51582}=\frac{51582}{186667}$

Thus, the conditional probability that he or she is in labor force if he or she is a college graduate is,

$$\begin{gathered} \frac{\frac{40390}{186667}}{\frac{51582}{186667}}=\frac{40390}{186667}\times \frac{186667}{51582} \\ =\frac{40390}{51582} \\ \approx 0.7830 \end{gathered}$$