An article on polygraph testing of FBI agents indicated that the probability of

Question

An article on polygraph testing of FBI agents indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is 0.2. Let x be the number of trustworthy FBI agents tested until someone fails the test. (Round your answers to four decimal places.) (a) Describe the probability distribution of x. O geometric O normal O binomial (b) What is the probability that the first false-positive will occur when the third person is tested? (e) 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? You may need to use the appropriate table in Appendix A to answer this question

Explanation / Answer

a) Geometric

b) P(3) = 0.8*0.8*0.2 = 0.128

c) P(Fewer than 4) = P(1) + P(2) + P(3) = 0.2 + 0.8*0.2 + 0.8*0.8*0.2 = 0.488

d) P(More than 3) = 1 - P(Less than or equal to 3) = 1 - 0.488 = 0.512

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