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Fingerprint expertise. Refer to the Psychological Science
Chapter 4, Problem 53E(choose chapter or problem)
Problem 53E
Fingerprint expertise. Refer to the Psychological Science (August 2011) study of fingerprint identification, Exercise 3.81 (p. 171). The 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 probability that a novice will correctly identify the match in all five pairs of fingerprints?
Questions & Answers
QUESTION:
Problem 53E
Fingerprint expertise. Refer to the Psychological Science (August 2011) study of fingerprint identification, Exercise 3.81 (p. 171). The 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 probability that a novice will correctly identify the match in all five pairs of fingerprints?
ANSWER:
Answer
Step 1 of 2
(a)
We have given 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.
We are asked to find the probability that an expert will correctly identify the match in all five pairs of fingerprints.
Let represents the number of pairs correctly identified by an expert in 5 trials.
Then the is a discrete random variable which follows a binomial distribution.
We know the definition of a binomial distribution,
If represent a random variable then we can define the binomial distribution as,
We have given
We need to find the probability
Hence,
Hence the probability that an expert will correctly identify the match in all five pairs of fingerprints is .