False positives where an individual fails even though he or

False positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results.

(a) If 8 random people take a polygraph test, what is the probability that none of the results are false positive?

(b) If 8 random people take a polygraph test, what is the probability that at least one of the results is false positive?

Solution

False positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results.

p=0.18

n=8

P(X=x) = (_nC_x) p^x (1-p)^n-x   

P(X=0) = (₈C₀) 0.15⁰ (1-0.15)^8-0   

P(X = 0) = 0.2725

(b) If 8 random people take a polygraph test, what is the probability that at least one of the results is false positive?

P( x >=1) = 1 - P(x=0)   = 1-0.2725 = 0.7275