A study by a reputable research organization found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 93% of the time. In contrast, a novice will correctly identify the match 76% of the time. Consider a sample of six different pairs of fingerprints, where each pair is a match. Complete parts a and b below.

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Chapter1: Combinatorial Analysis
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A study by a reputable research organization found that when presented with prints from the same individual, a fingerprint
expert will correctly identify the match 93% of the time. In contrast, a novice will correctly identify the match 76% of the time.
Consider a sample of six different pairs of fingerprints, where each pair is a match. Complete parts a and b below.
a. What is the probability that an expert will correctly identify the match in all six pairs of fingerprints?
The probability is:
(Round to four decimal places as needed.)
b. What is the probability that a novice will correctly identify the match in all six pairs of fingerprints?
The probability is :
(Round to four decimal places as needed.)
Transcribed Image Text:Question Help A study by a reputable research organization found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 93% of the time. In contrast, a novice will correctly identify the match 76% of the time. Consider a sample of six different pairs of fingerprints, where each pair is a match. Complete parts a and b below. a. What is the probability that an expert will correctly identify the match in all six pairs of fingerprints? The probability is: (Round to four decimal places as needed.) b. What is the probability that a novice will correctly identify the match in all six pairs of fingerprints? The probability is : (Round to four decimal places as needed.)
Expert Solution
Step 1

Given data:

The probability that fingerprint experts correctly identify the match is P(A)=93%=0.93.

The probability that novice correctly identifies the match is P(B)=76%=0.76.

The numbers of pairs are n=6.

(a)

The expression for the probability that the expert identifies all the match of six pairs is,

PE=PA6

Substitute the given values in the above expression.

PE=0.936=0.6470

 

Thus, the probability that the expert identifies all the matches of six pairs is 0.647.

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