Question

A study found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. In contrast, a novice will correctly identify the match 75% of the time. Consider a sample of five different pairs of fingerprints, where each pair is a match.A) What is the probability that an expert will correctly identify the match in all five pairs of fingerprints?B) What is the probablity that a novice will correctly identifity the match in all five pairs of fingerprints?

Answer 1

a) probability that an expert will correctly identify the match in all five pairs of fingerprints =0.6591 = 65.9%

b) probability that a novice will correctly identify the match in all five pairs of fingerprints =0.2373 = 23.7%

Explanation:

from the question, probability that the expert gets the fingerprint right say Pr(expert1) is 92% that is 0.92

and probability that the novice gets the fingerprint right say Pr(novice1) is 75% that is 0.75.

given 5 fingerprints,

a) the probability that the expert gets them all right say Pr(expert5) = probability that the expert gets one right raised to the power 5

i.e Pr(expert5) = Pr(expert1)^5

= (0.92)^5 = 0.6591 = 65.9%

b) the probability that the novice gets them all right say Pr(novice5) = probability that the novice gets one right raised to the power 5

i.e Pr(novice5) = Pr(novice1)^5

=(0.75)^5 = 0.2373 = 23.7%