Chapter 7.3, Problem 71E

To determine

Tocalculate:The probability that he or she is in labor force if a randomly chosen person 25 years of age or older is a college graduate.

Answer to Problem 71E

The required probability is 0.7830.

Explanation of Solution

Given information:

The data:

Highest education	Total population	In labor force	Employed
Didn’t finish high school	27,669	12,470	11,408
High school but no college	59,860	37,834	35,857
Less than bachelor’s degree	47,556	34,439	32,977
College graduate	51,582	40,390	39,293

Formula used:

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

Calculation:

Know that 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 labor force and college graduate is,

  $\frac{40390}{\begin{array}{l}27669+59860+47556+51582\\ \end{array}}=\frac{40390}{186667}$

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,

  $\begin{array}{c}\frac{\frac{40390}{186667}}{\frac{51582}{186667}}=\frac{40390}{\cancel{186667}}\times \frac{\cancel{186667}}{51582}\\ =\frac{40390}{51582}\\ \approx 0.7830\end{array}$

Hence, the required probability is 0.7830.