Urn Problem - Historical Remarks

Historical Remarks

In Ars Conjectandi (1713), Jacob Bernoulli considered the problem of determining, given a number of pebbles drawn from an urn, the proportions of different colored pebbles within the urn. This problem was known as the inverse probability problem, and was a topic of research in the eighteenth century, attracting the attention of Abraham de Moivre and Thomas Bayes.

Bernoulli used the Latin word urna, which primarily means a clay vessel, but is also the term used in ancient Rome for a vessel of any kind for collecting ballots or lots; the present-day Italian word for ballot box is still urna. Bernoulli's inspiration may have been lotteries, elections, or games of chance which involved drawing balls from a container, and it has been asserted that

Elections in medieval and renaissance Venice, including that of the doge, often included the choice of electors by lot, using balls of different colors drawn from an urn.

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