Chapter 7.3, Problem 78E

(a)

To determine

To find: the probability that a randomly chosen person 25 years of age or older is in the labour force.

Answer to Problem 78E

67.035%

Explanation of Solution

Given:

Highest education	Total population	In labour 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:

  $\text{Probability=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}$

Calculation:

The table contains $27,669+59,860+47,556+51,582=186,667$ people in total, where $12,470+37,834+34,439+40,390=125,133$ of the $186,667$ people are in the labour force.

  $\begin{array}{c}P\left(\text{In the labor force}\right)=\frac{\text{favorable outcomes}}{\text{possible outcomes}}\\ =\frac{125,133}{186,667}\\ =0.67035\\ =67.035\%\end{array}$

(b)

To determine

To Calculate: the probability that he or she is in the labour force.

Answer to Problem 78E

78.30%

Explanation of Solution

Given:

Highest education	Total population	In labour 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:

  $\text{Probability=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}$

Calculation:

There are 51582 college graduates which is given in the row “college graduate” and in the column “Total population” of the given. 40390 Of the 51582 college graduates are in the labour force, which is given in the row “college graduate “and in the column “in labour force” of the given table.

  $\begin{array}{c}P\left(\text{In labor force college graduate}\right)=\frac{\#\text{}\text{ of favorable outcomes}}{\#\text{ of possible outcomes}}\\ =\frac{40,390}{51,582}\\ =\frac{20,195}{25,791}\\ =0.7830\\ =78.30\%\end{array}$

(c)

To determine

To find: the event “in the labour force” and collage graduate” independent.

Answer to Problem 78E

Not independent

Explanation of Solution

Given:

Highest education	Total population	In labour 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:

  $\text{Probability=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}$

Calculation:

The table contains $27,669+59,860+47,556+51,582=186,667$ people in total, while $12,470+37,834+34,439+40,390=125,133$ of the $186,667$ people are in the labor force.

  $\begin{array}{c}P\left(\text{In the labor force}\right)=\frac{\#\text{}\text{ of favorable outcomes}}{\#\text{ of possible outcomes}}\\ =\frac{125,133}{186,667}\\ =0.67035\\ =67.035\%\end{array}$

There are 51582 college graduates which is given in the row “college graduate” and in the column “Total population” of the given table.40390 of the 51582 college graduates are in the labor force, which is given in the row “college graduate “and in the column “ in labor force” of the given

  $\begin{array}{c}P\left(\text{In labor force college graduate}\right)=\frac{\#\text{}\text{ of favorable outcomes}}{\#\text{ of possible outcomes}}\\ =\frac{40,390}{51,582}\\ =\frac{20,195}{25,791}\\ =0.7830\\ =78.30\%\end{array}$

Two events are independent, if the probability that one event happen in no way effects the probability of the other event occurring.

Since the probabilities $P$ (in labour force college graduate) are not equal, the probability of the event “in the labour force” is affected when the event “college graduate” happens and therefore the events are not independent.