# Question: Fingerprints are now widely accepted as a form of identi cation

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 1/2.

(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?

(b) Galton further estimated that the likelihood of determining the ﬁngerprint type (e.g., arch, left loop, whorl, etc.) as (1/2)4 and the likelihood of the occurrence of the correct number of ridges entering and exiting each of the 24 regions as (1/2)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).

(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?

(b) Galton further estimated that the likelihood of determining the ﬁngerprint type (e.g., arch, left loop, whorl, etc.) as (1/2)4 and the likelihood of the occurrence of the correct number of ridges entering and exiting each of the 24 regions as (1/2)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).

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