Fingerprint expertise, refer to the Psychological Science (August 2011) study of fingerprint identification, exercise 3.85 (p.200). The study found that when presented with prints from same individual, a fingerprint expert will correctly identify the match 92% of the time, In contract, 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 probability that an expert will correctly identify the match in all five pairs of fingerprints?

A fingerprint expert will correctly identify the match 92% of the time, so probability of success is 92%, so \(\)\(p = 92\% = 0.92\).

And a sample of five different pairs of fingerprints are taken, so \(n = 5\).

The binomial distribution is the probability of exact success on n repeated trials, the probability of success is p, and probability of failure is q, then the binomial probability can be written as

\({}^n{C_x}{p^x}{q^{n - x}}\).

a):

Each attempt of identifying the match is independent, and there are 5 different pairs of fingerprints are given, so there are 5 attempts.

The one term for each attempt, the probabilities are to be multiplied.

So, the probability that the expert will identify every pair correctly is

\(\begin{array}{l} &= 0.92 \times 0.92 \times 0.92 \times 0.92 \times 0.92\\ &= {0.92^5}\\ &= 0.65908\end{array}\)

The probability that the expert will identify every pair correctly is 0.66.