E412 -- Solution d'une question très difficile dans le calcul des probabilités
(Solution to a very difficult question in the calculus of probabilities)
The Genoise lottery was the first number lottery and as such drew much attention from 18th Century mathematicians. Its chief expositors were Nicolas Bernoulli and Euler. Euler himself devoted at least five papers to the subject:
as well as this one. In this paper Euler analyzes a lottery in which there are several classes of prizes and a guaranteed payment.
According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on November 29,
Originally published in Memoires de l'academie des sciences de Berlin 25, 1771, pp. 285-302
Opera Omnia: Series 1, Volume 7, pp. 162 - 180
- Original publication: E412
- E412 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
- Richard J. Pulskamp has put together a fantastic page on Euler's Probability & Statistics, including a lot of interesting background and historical work. The page includes a
translation of E412.
- Rob Bradley
of Adelphi Univeristy has written an excellent paper,
Euler and the Genoese Lottery
in which he examines a significant fraction of Euler's work on probability.
- Euler wrote four other papers on the Genoese lottery:
- E338, Sur la probabilte des sequences dans la lotterie Genoise
- E600, Solutio quarundam quaestionum difficilorum in calculo probabilis
- E812, Relexiones sur une espese singulier de loterie nommee loterie genoise
- E813, Analyse d'un probleme du calcul des probabilites
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