Question

James Burke states that there is a 72% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 7% chance that the polygraph will falsely accuse someone of lying.

Required:
a. Suppose a person answers 87% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?
b. Suppose a person answers 13% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?

Answer 1

a. The polygraph will wrongly indicate 0.91% of answers as lies. b. The polygraph will correctly indicate 9.36% of answers as lies.

Step-by-step explanation:

a. In this case, the person answers 87% of the questions truthfully, which means 13% of the answers are lies. The polygraph has a 7% chance of falsely accusing someone of lying. Therefore, the percentage of answers that the polygraph will wrongly indicate as lies is:

(% of lies) * (chance of false accusation) = 13% * 7% = 0.91%

b. Similarly, if the person answers 13% of the questions with lies, then the percentage of answers that the polygraph will correctly indicate as lies is:

(% of lies) * (chance of detection) = 13% * 72% = 9.36%

Answer 2

a) 6.09 %

b) 9.36 %

Step-by-step explanation:

a) Given

% of questions that are truthful = 87% = -.87

% of right questions that are falsely indicated as lies = 7%

Percentage of the answers that the polygraph wrongly indicate as lies = 0.87 * 0.07 = 0.0609 = 0.1 = 10%

b) % of answers that are lies = 13% = 0.13

% of answers that are correctly caught as lies = 72%

percentage of the answers that the polygraph will correctly indicate as lies

= 0.13 * 0.72 = 0.0936 = 0.1 = 10 %