In his book Chances: Risk and Odds in Everyday Life, James Burke states that the
ID: 3126228 • Letter: I
Question
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?
(c) Repeat parts (a) and (b) if 48% of the questions are answered truthfully and 52% are answered with lies.
(d) Repeat parts (a) and (b) if 14% of the questions are answered truthfully and the rest are answered with lies.
(a) % (b) %Explanation / Answer
Let
T = answers truthfully
L = indicated as lie
a)
P(L n T) = P(T) P(L|T) = 0.86*0.07 = 0.0602 = 6.02% [ANSWER]
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b)
P(T' n L) = P(T') P(L|T') = 0.14*0.72 = 0.1008 = 10.08% [ANSWER]
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c)
a)
P(L n T) = P(T) P(L|T) = 0.48*0.07 = 0.0336 = 3.36% [ANSWER]
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b)
P(T' n L) = P(T') P(L|T') = 0.52*0.72 = 0.3744 = 37.44% [ANSWER]
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d)
a)
P(L n T) = P(T) P(L|T) = 0.14*0.07 = 0.0098 = 0.98% [ANSWER]
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b)
P(T' n L) = P(T') P(L|T') = 0.86*0.72 = 0.6192 = 61.92% [ANSWER]