Chapter 6, Problem 1CRE

For Exercises 1–7, use the data in the following table that shows results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct.

1. If one of the subjects is randomly selected, find the probability of selecting someone who lied.

To determine

Compute the probability of selecting a person who lied.

Answer to Problem 1CRE

The probability of selecting a person who lied is 0.520.

Explanation of Solution

Calculation:

The given information is a table which provide the idea about number of person lied or not and corresponding results in the polygraph.

The probability of an event is the chance of occurrence of that event. The probability of an event A is denoted by $P\left(A\right)$ and is obtained by the formula:

$P\left(A\right)=\frac{\text{Number of ways event occurs}}{\text{Total number of sample points}}$

Event A denotes the event that the selected person lied.

$\begin{array}{c}\text{Total number of person }=15+42+32+9\\ =98\end{array}$

$\begin{array}{c}\text{Total number of person}\text{lied }=42+9\\ =51\end{array}$

Substitute 51 for “number of ways event A occurs” and 98 for “Total number of outcomes” in the probability formula.

Therefore,

$\begin{array}{c}P\left(A\right)=\frac{51}{98}\\ =0.520\end{array}$

The probability of selecting a person who lied is 0.520.