Chapter 7.3, Problem 72E

To determine

To find: Whether the events “in the labor force” and “college graduate” are independent events or not

Answer to Problem 72E

No, they are not independent

Explanation of Solution

Given:

Highest education	Total population	In labour force	Employed
Did not finish high school	27669	12470	11408
High school but no college	59860	37834	35857
Less than bachelor's degree	47556	34439	32977
College graduate	51582	40390	39293

Concept used:

It is known that; two events A and B can be considered as independent if:

  $P\left(A|B\right)=P\left(A\right)$

Calculation:

The probabilities could be calculated as:

  $\begin{array}{c}P\left(\text{Labor force | College graduate}\right)=\frac{125133}{186667}\\ =0.6704\\ P\left(\text{Labor foce}\right)=\frac{125133}{186667}\\ =0.6704\end{array}$

Here,

  $\begin{array}{c}P\left(\text{Labor force| College graduate}\right)\ne P\left(\text{Labor force}\right)\\ 0.7830\ne 0.6704\end{array}$

Thus, two events are not independent events.