The manufacturer of a lie detector claims that it is 90% accurate. The St. John\

Question

The manufacturer of a lie detector claims that it is 90% accurate. The St. John' s police department isn' t convinced, so they ask the manufacturer to test its machine on ten suspects. Assume the suspects' responses are independent. a) Assume that the manufacturer's claim is true. What is the probability that the lie detector will correctly determine the truth for all ten suspects? b) Assume that the manufacturer's claim is true. What is the probability that the lie detector will yield an incorrect result for at least two of the ten suspects?

Explanation / Answer

a) P( Correct on all 10) = 0.9^10=0.3486

b) P( atleast 2 incorrect)=1-P( 0 incorrect+1 incorrect) = 1-0.8^10-10*0.2*0.8^9=0.62419

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