The article on polygraph testing of FBI agents referenced in Exercise 7.51 indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is .15. Let x be the number of trustworthy FBI agents tested until someone fails the test.
a. What is the probability distribution of x?
b. What is the probability that the first false-positive will occur when the third person is tested?
c. What is the probability that fewer than four are tested before the first false-positive occurs?
d. What is the probability that more than three agents are tested before the first false-positive occurs?