Question

Use the sample data in the table. Results from Experiments with Polygraph Instruments Did the Subject Actually Lie? No Yes (Did Not (Lied) Lie) 15 42 (false (true positive) positive) Positive test result (Polygraph test indicated that the subject lied.) Negative test result (Polygraph test indicated that the subject did not 32 9 (true (false negative) negative) lie.) If 3 of the 98 test subjects are randomly selected without replacement, find the probability that they all had false positive results. Is it unusual to randomly select 3 subjects without replacement and get 3 results that are all false positive results? Why?

Answer 1

Let F be the selected person had false positive results

And number of false positive = 15

Now,

Number of ways of selecting r items out of n items = n C r

Therefore,

Yes, since
0.00299 < 0.05
getting all 3 subjects who had false positives would be unusual.