A new? lie-detector test has been devised and must be tested before it is put in

Question

A new? lie-detector test has been devised and must be tested before it is put into use. Three hundred people are selected at? random, and each person draws and keeps a card from a box of 300 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who? lied, 70?% fail the new? lie-detector test? (that is the test indicated? lying). Of those who told the? truth, 5?% failed the test.

What is the probability that a randomly chosen subject will have lied given that the subject failed the? test? That the subject will not have lied given that the subject failed the? test?

Explanation / Answer

Based on given data, the contigency table is created as below,

Total persons who lie = Total persons who do not lie (tell truth) = 150

Of those who? lied, 70?% fail the new? lie-detector test?.

Then, total persons who lied and fail the test = 150 * 0.7 = 105

and total persons who lied and do not fail the test = 150 - 105 = 45

Of those who told the? truth, 5?% failed the test.

Then, total persons who do not lied and fail the test = 150 * 0.05 = 105

and total persons who do not lied and do not fail the test = 150 - 7.5 = 142.5

Total persons who fail the test = 105 + 7.5 = 112.5

Total persons who do not fail the test = 45 + 142.5 = 187.5

Probability that a randomly chosen subject will have lied given that the subject failed the? test = 105 / 112.5 = 0.9333

Probability that a randomly chosen subject will not have lied given that the subject failed the? test = 7.5 / 112.5 = 0.0667

Lie Do not Lie Total Fail the test (test indicated? lying) 105 7.5 112.5 Do not fail the test (test do not indicate lying) 45 142.5 187.5 Total 150 150 300

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