Sir Francis Galton (1822- 1911) was educated as a physician but had the time, money, and inclination for research on whatever interested him, and almost everything did. Though not the first to notice that he could find no two people with the same fingerprints, he was the first to develop a system for categorizing fingerprints and to persuade Scotland Yard to use fingerprints in criminal investigation. He supported his argument with fingerprints of friends and volunteers solicited through the newspapers, and for all comparisons P(fingerprints match) ¼ 0. To compute the number of events associated with Galton's data:
a. Suppose fingerprints on only 10 individuals are involved.
i. How many comparisons between individuals can be made? However, for the second individual there are only 8 additional comparisons because his fingerprints have already been compared to the first.
ii. How many comparisons between fingers can be made? Assume these are between corresponding fingers of both individuals in a comparison, right thumb of one versus right thumb of the other, and so on.
b. Suppose fingerprints are available on 11 individuals rather than 10. Use the results already obtained to simplify computations in finding the number of comparisons among people and among fingers.