47. In three careful studies, lie detector experts examined several persons, som

Question

47. In three careful studies, lie detector experts examined several persons, some of which are known to be truthful and others known to be lying, to see if the experts could tell which were which. Overall, 88% of the liars were pronounced "deceptive" and 67% of the truthful people were judged honest." Using these data and assuming that 85%of the people tested are truthful and 15% are lying, what is the probability that a person pronounced "deceptive" is in fact truthful? a. b. What is the probability that a person judged "honest" is in fact lying? How would these two probabilities be altered if half of the people are truthful and half are lying? c. Probability of being judged "deceptive" when truthful 50u Probability of being judged "honest" when lying lavo

Explanation / Answer

a) Let the total number of people who were in the test be P.

Given: 0.85P are truthful people and 0.15P are liars.

Also, 88% of the liars were pronounced "deceptive" which means -> 12% of the liars were pronounced "honest"

and 67% of the truthful people were pronounced "honest" which means -> 33% of the truthful people were judged "deceptive"

Putting that into a table:

P(person pronounced deceptive, is in fact truthful) = 0.2805P/P = 0.2805

Ans: 0.2805

b) P(person pronounced honest, is in fact lying) = 0.018P/P = 0.018

Ans: 0.018

c) In this case, number of truthful people = 0.5P and number of liars = 0.5P

Probability of being judged deceptive when truthful = 0.33(0.5P) / P = 0.165P/P = 0.165

Ans: 0.165

Probability of being judged honest when lying = 0.12(0.5P) / P = 0.06P/P = 0.06

Ans: 0.06

Cheers!

Upvote if this was helpful!

Truthful Liars Honest 0.67(0.85P) = 0.5695P 0.12(0.15P) = 0.018P Deceptive 0.33(0.85P) = 0.2805P 0.88(0.15P) = 0.132P

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