Question

The FBI kept records of people who were given polygraph tests and found that 15% of the trustworthy people fail the test.

a. Ten trustworthy people just took the polygraph test, what is the probability that all 10 pass?

b. What is the probability that more than 2 of the 10 fail?

Answer 1

P(fail) = 0.15

P(pass) = 1 - 0.15 = 0.85

a) P(all 10 pass) = 0.85¹⁰ = 0.1969

b) p = 0.15

n = 10

This is a binomial distribution.

P(X = x) = 10Cx * 0.15^x * (1 - 0.15)^10-x

P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

              = 1 - (10C0 * 0.15⁰ * 0.85¹⁰ + 10C1 * 0.15¹ * 0.85⁹ + 10C2 * 0.15² * 0.85⁸ )

              = 1 - 0.8202

              = 0.1798