...also in Neyman, 1952, pp. 15-18) concerns the chance that a chord drawn "at random" to a circle will be longer than the side of an equilateral triangle inscribed in the circle. If the angle the chord makes to a given line is taken to measure the range of possibilities, the chance...

...outcomes !*• infinite resulted in seemingly even greater difficulties. That was dramatized by Bennind. who considered the problem of finding the probability...of the circumference of the circle as being the set fi of all possible outcome^ and the arc between the other two vertices as the set A of "favorable outcomes"...

...(Bertrand's Paradox). A chord is drawn at random in a circle. Find the probability that the chord is longer than the side of an equilateral triangle inscribed in the circle. First Solution Draw the chord AB and a tangent CD at A to the circle (Fig. 9). Let в be angle between...

...famous French mathematician. What is the probability that a chord drawn at random inside a circle will be longer than the side of an equilateral triangle inscribed in the circle? We can answer as follows. The chord must start at some point on the circumference. We call this point...

...greater than V3 times the radius of the circle? In other words, what is the probability that AB is longer than the side of an equilateral triangle inscribed in the circle? (Call this proposition E.) Bertrand provides three incompatible solutions to this problem, each one...