Paradoxes in elementary probability theory

U ovom diplomskom radu odabrano je i opisano nekoliko poznatih i zanimljivih vjerojatnosnih paradoksa: Monty Hall i njemu slični paradoksi, paradoks intranzitivnih kocaka, Bertrandov paradoks geometrijske vjerojatnosti, popularni rođendanski paradoks prikladan za primjenu u školskoj matematici te problem dviju omotnica kod kojeg paradoks leži u sugeriranom objašnjenju. Na samom kraju obrađen je Sankt-Peterburški paradoks za koji se rješenja predlažu zadnjih 300 godina, a neki prijedlozi rješenja imali su važan utjecaj na razvoj ekonomije. Pojava raznih paradoksa i rasprava o njihovim mogućim rješenjima tijekom korespondencije matematičara u razdoblju renesanse postavile su temelje suvremene teorije vjerojatnosti. Neki od paradoksa potaknuli su razvoj interdisciplinarnih znanosti i time omogućili napredak područja koja nisu usko vezana samo uz matematiku. Ti rezultati imaju utjecaj na vrijeme u kojemu živimo, a s obzirom da neki još nisu definitivno razrješeni, zasigurno će nastaviti svoj utjecaj i na vremena koja tek dolaze.In this thesis, several well known and interesting paradox are selected and described: the Monty Hall and similar paradoxes, intransitive dice paradox, Bertrand’s paradox on geometric probability, the popular birthday problem, suitable for implementation in school mathematics, and the two envelopes problem, where the paradox lies in a possible misleading explanation. At the very end, the thesis studies the Saint Petersburg paradox, which has been discussed for the last 300 years and some proposed solutions had an important impact on the development of the economics. The emergence of various paradoxes and discussions of their possible solutions during the correspondence of mathematicians in the Renaissance period laid the foundations of modern probability theory. Some of the paradoxes have spurred the development of interdisciplinary sciences and thus enabled the advancement of areas that are not closely related to mathematics alone. These results have an impact on the times we are living in, but since some have not yet been fully resolved, they will certainly continue to have an impact on the times yet to come