A fingerprint matching system uses an algorithm (T) to \"match\" fingerprints to

Question

A fingerprint matching system uses an algorithm (T) to "match" fingerprints together under comparison. The system can come up with a "positive match" T+ or a "negative match" T-. The fingerprints under comparison can truly be from the same person M+ or not M-. The matching system has the following performance characteristics: The true positive rate of the matcher is: Pr(T+ | M+) = 0.95 The false positive rate of the matcher is: Pr(T+ | M-) = 0.003 The probability that any two randomly selected fingerprints from different people in the human population will "match" is conservatively estimated by experts as: Pr(M-) = 0.000001 What is the probability the matcher will come up with a "positive match" on any given comparison, Pr(T+)? What is the true negative rate of the matcher? Compute Pr(M+|T+): Compute Pr(M-|T+) Compute Pr(M-|T-)

Explanation / Answer

We are representing Pr by P...

(a) P(T+) = P(M+)*P(T+ | M+) + P(M-)*P(T+ | M-) = (1-0.000001)*0.95 + 0.000001*0.003 = 0.949999905

(b) P(T-) = 1-P(T+) = 1 - 0.94999905 = 0.05

(c) P(M+ | T+) =P(T+ | M+) * P(M+) / P(T+) = 0.95 * (1 - 0.000001) / 0.94999905 = 0.99999999

(d) P(M- | T+) = 1 - P(M+ | T+) = 0.00000001

(e) P (M- | T-) = P(T- | M-) * P(M-) / P(T-) = 0.997 * 0.000001 / 0.05 = 0.00001993

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