?Fingerprints Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link th

Chapter 5, Problem 32

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Fingerprints Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link the owner to the computer. In 1892, Sir Francis Galton explored the use of fingerprints to uniquely identify an individual. A fingerprint consists of ridgelines. Based on empirical evidence, Galton estimated the probability that a square consisting of six ridgelines that covered a fingerprint could be filled in accurately by an experienced fingerprint analyst as ½.

(a) Assuming that a full fingerprint consists of 24 of these squares, what is the probability that all 24 squares could be filled in correctly, assuming that success or failure in filling in one square is independent of success or failure in filling in any other square within the region? (This value represents the probability that two individuals would share the same ridgeline features within the 24-square region.)

(b) Galton further estimated that the likelihood of determining the fingerprint type (e.g., arch, left loop, whorl, etc.) as 4 and the likelihood of the occurrence of the correct number of ridges entering and exiting each of the 24 regions as 8. Assuming that all three probabilities are independent, compute Galton’s estimate of the probability that a particular fingerprint configuration would occur in nature (that is, the probability that a fingerprint match occurs by chance).