These are the results from experiments with polygraph instruments. Did the Subje
ID: 3252890 • Letter: T
Question
These are the results from experiments with polygraph instruments.
Did the Subject Actually Lie?
No (Did Not Lie)
Yes (Lied)
Positive Test Result
(Polygraph test indicated that the subject lied.)
15
(false positive)
42
(true positive)
Negative Test Result
(Polygraph test indicated that the subject did not lie.)
32
(true negative)
9
(false negative)
a) If one of the responses is randomly selected, what is the probability that it is a false positive? What does this probability suggest about the accuracy of the polygraph test?
b) If one of the responses is randomly selected, what is the probability that it is not a lie?
c) If one of the test subjects is randomly selected, find the probability that the subject had negative test result.
d) If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or lied.
e) If two of the subjects are randomly selected without replacement, find the probability that the first selected person had a positive test result and the second selected person had a negative test result.
f) If 2 of the test subjects are randomly selected without replacement, find the probability that both had false negative test results. Is it unusual to randomly select 2 subjects without replacement and get 2 results that are all false negative test results?
No (Did Not Lie)
Yes (Lied)
Positive Test Result
(Polygraph test indicated that the subject lied.)
15
(false positive)
42
(true positive)
Negative Test Result
(Polygraph test indicated that the subject did not lie.)
32
(true negative)
9
(false negative)
Explanation / Answer
a) If one of the responses is randomly selected, what is the probability that it is a false positive? What does this probability suggest about the accuracy of the polygraph test?
probability of false positive = 15/98 = 0.153
b) If one of the responses is randomly selected, what is the probability that it is not a lie?
probability that it is not a lie = 47/98
c) If one of the test subjects is randomly selected, find the probability that the subject had negative test result.
probability negative test result = 41/98
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