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3.1 Sets & Set Diagrams

3.1 Sets & Set Diagrams
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  • Math Help

    Example 4 is for illustration only. The numbers used in the example are hypothetical.

    The goal of the example is to illustrate that a 6-point match between two fingerprints is not sufficient to conclude that the fingerprints came from the same person.

    There is no agreement on how many points need to match to conclude that two fingerprints come from the same individual. According to the National Institute of Standards and Technology, a latent fingerprint will usually have at least 12 minutiae points in common with a file fingerprint. Complete fingerprints will usually match on at least 50 minutiae points.

  • Consumer Suggestion

    Fingerprinting was first used by the ancient Babylonians to record business transactions. The ancient Chinese also used it for business and identifying children. Using fingerprints to identify criminals began in the late 19th century and was first used as court evidence in 1902. The FBI's Identification Division maintains the Integrated Automated Fingerprint Identification System. The IAFIS contains criminal histories and fingerprints for more than 70 million subjects in the criminal file, including 73,000 known or suspected terrorists worldwide.

    For more information about the collection and matching of fingerprints, visit the National Institute of Standards and Technology.

  • Checkpoint Solution
    You can continue the pattern in Example 4 as follows.


    1 billion people have Point 1

    20 % of these also have Point 2

    20 % of these also have Point 3

    20 % of these also have Point 4

    20 % of these also have Point 5

    20 % of these also have Point 6

    20 % of these also have Point 7

    20 % of these also have Point 8

    20 % of these also have Point 9

    20 % of these also have Point 10

    20 % of these also have Point 11

    20 % of these also have Point 12

    1,000,000,000 people

    200,000,000 people

    40,000,000 people

    8,000,000 people

    1,600,000 people

    320,000 people

    64,000 people

    12,800 people

    2,560 people

    512 people

    102 people

    20 people

    1-point match

    2-point match

    3-point match

    4-point match

    5-point match

    6-point match

    7-point match

    8-point match

    9-point match

    10-point match

    11-point match

    12-point match

    So, using the hypothesis that any two people have a 20% likelihood of matching one and two fingerprint points, there are up to 20 people out of a billion that have a 12-point match.

    If you continue this pattern for 16 points, you will see there is an even greater likelihood the two fingerprints "absolutely" came from the same person.

  • Comments (1)

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    system user
    Ron Larson (author)7 years ago |
    When I was writing this book, there were many times when my mind would wander and think about happy or sad things that have happened to people. When I was researching and writing this example, I thought about the tragic miscarriages of justice in which innocent people have been convicted of crimes in which the condemning evidence was a fingerprint "match" based on too few points.
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