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In his book Chances: Risk and Odds in Everyday Life, 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.

(a) Suppose a person answers 86% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?


(b) Suppose a person answers 14% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?

Respuesta :

Answer:

a) 6.02%

b) 10.08%

Step-by-step explanation:

We have these following percentages:

If the person is lying, a 72% chance that the polygraph catches her.

If the person is telling the truth, a 7% chance that the polygraph says that the person is lying.

(a) Suppose a person answers 86% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?

This is 7% of 86%. So

[tex]P = 0.07*0.86 = 0.0602[/tex]

(b) Suppose a person answers 14% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?

This is 72% of 14%. So

[tex]P = 0.72*0.14 = 0.1008[/tex]

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