Bertrand’s paradox an inconsistency arising from the classical definition of an event’s probability as the number of favorable cases divided by the number of possible cases. Given a circle, a chord is selected at random. What is the probability that the chord is longer than a side of an equilateral triangle inscribed in the circle? The event has these characterizations: (1) the apex angle of an isosceles triangle inscribed in the circle and having the chord as a leg is less than 60°, (2) the chord intersects the diameter perpendicular to it less than ½ a radius from the circle’s center, and (3) the chord’s midpoint lies within a circle concentric with the original and of ¼ its area. The definition thus suggests that the event’s probability is 1/3, 1/2, and also ¼. Joseph Bertrand, a French mathematician, published the paradox in Calcul des probabilités (1889). See also PROB- ABILIT. P.We.