Question

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?

Short answer

a) The probability that an expert will correctly identify the match in all five pairs of fingerprints 0.66

Step-by-step solution

Given information

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 \(n = 5\).

Concepts

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

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

Explanation

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.