Editing Urn problem (section)

==History==

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 ''[[wikt:urna#Latin|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 language|Italian]] or [[Spanish language|Spanish]] word for [[ballot box]] is still ''[[wikt:urna#Italian|urna]]''. Bernoulli's inspiration may have been [[lottery|lotteries]], [[election]]s, 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 of Venice|doge]], often included the [[Sortition|choice of electors by lot]], using balls of different colors drawn from an urn.<ref name="dogeelection">{{cite web |author1=Mowbray, Miranda |author2=Gollmann, Dieter |name-list-style=amp |title=Electing the Doge of Venice: Analysis of a 13th Century Protocol |url=http://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.html |access-date=July 12, 2007 }}</ref>