Question

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 94​% of the time. In​ contrast, a novice will correctly identify the match 74​% 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 seven pairs of​ fingerprints?
b. What is the probability that an novice will correctly identify the match in all seven pairs of​ fingerprints?

Answer 1

Answer:

a. 0.6899

b. 0.1642

Step-by-step explanation:

a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.94\times0.94\times0.94\times0.94\times0.94\times0.94\\\\=0.6899$

Hence, the probability of correctly identifying the 6 matches is 0.6899

b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.74\times0.74\times0.74\times0.74\times0.74\times0.74\\\\=0.1642$

#Hence, the probability of correctly identifying the 6 matches is 0.1642

*I have used the sample size of 6(due to conflicting info/question size).