The solution would be like this for this specific problem:
Given:
No (Did Not Lie) Yes (Lied)
Positive Test Result 10 29
(Positive test indicated that the subject lied.) (false positive) (true positive)
Negative test result 66 18
(Polygraph test indicated that the subject did not lie.) (true negative) (false negative)
Find:
The probability that all four test subjects had a true negative test result when they are randomly selected without replacement.
Formula:
(66/123) x (65/122) x (64/121) x (63/120) = 0.0793864272
Therefore, when they are randomly selected without replacement, the probability that all four test subjects had a true negative test result is 0.079.