Bertrand's paradox


Bertrand's paradox
Paradox described in the Calcul des probabilités (1889) of the French probabilist J. Bertrand (1822–1900). What is the probability that a chord drawn at random in a circle is longer than the side of an equilateral triangle whose three corners touch the circle? It is longer if its midpoint falls nearer the circumference than the centre of a radius bisecting it, so the probability is ½. Keeping one end of the chord fixed, it is longer if the angle at which it is drawn is within the 60° arc of the triangle, so the probability is 1/3. Or, it is longer if its midpoint lies in the area of the inner circle with radius one half of the original; this circle occupies one quarter of the area of the original, so the chance is 1/4. Bertrand used the paradox to show that there is no unique best way of applying the principle of indifference to such a case.

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • Bertrand's paradox — There are three different paradoxes called Bertrand s paradox or the Bertrand paradox: * Bertrand s paradox (probability) * Bertrand paradox (economics) * Bertrand s box paradox …   Wikipedia

  • Bertrand's paradox (probability) — Bertrand s paradox is a problem within the classical interpretation of probability theory. Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer …   Wikipedia

  • Bertrand paradox (economics) — For other paradoxes by Joseph Bertrand, see Bertrand s paradoxIn economics and commerce, the Bertrand paradox ndash; named after its creator, Joseph Bertrand ndash;describes a situation in which two players (firms) reach a state of Nash… …   Wikipedia

  • Bertrand, Joseph — ▪ French mathematician and educator in full  Joseph Louis François Bertrand  born March 11, 1822, Paris, France died April 5, 1900, Paris       French mathematician and educator remembered for his elegant applications of differential equations… …   Universalium

  • Bertrand's box paradox — is a classic paradox of elementary probability theory. It was first posed by Joseph Bertrand in his Calcul des probabilités , published in 1889. There are three boxes: a box containing two gold coins, a box with two silver coins, and a box with… …   Wikipedia

  • Bertrand Russell — Saltar a navegación, búsqueda Bertrand Arthur William Russell, 3er Conde de Russell Russell en 1907 Filosofía Occidental Filosofí …   Wikipedia Español

  • Bertrand competition — is a model of competition used in economics, named after Joseph Louis François Bertrand (1822 1900). Specifically, it is a model of price competition between duopoly firms which results in each charging the price that would be charged under… …   Wikipedia

  • Bertrand Russell — Infobox Philosopher region = Western Philosophy era = 20th century philosophy color = #B0C4DE image caption = Russell in 1907 image size = 150px name = Bertrand Arthur William Russell, 3rd Earl Russell birth = birth date|df=yes|1872|5|18 Trellech …   Wikipedia

  • Paradox — Ein Paradoxon oder Paradox (altgriechisch παράδοξον, von παρα , para – gegen und δόξα, dóxa – Meinung, Ansicht), auch Paradoxie (παραδοξία) und in der Mehrzahl Paradoxa g …   Deutsch Wikipedia

  • Bertrand-Paradox — Der Bertrand Wettbewerb wurde als Modell von Joseph Bertrand für die Wettbewerbsform des Oligopols in seiner einfachsten Form als Duopol entwickelt. Es handelt sich um eine Weiterentwicklung des Cournot Oligopols. Der wesentliche Unterschied ist… …   Deutsch Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.