Bertrand's experiment generates a random chord of the circle of radius 1 center at the origin. In the simulation, one point of the chord is fixed at \((0, 1)\) and the other is the random point \((X, Y)\). Random variable \(D\) is the length of the line segment from the center of the circle to the center of the chord, and random variable \(A\) is the angle that this line segment makes with the horizontal. Random variable \(I\) indicates the event that the chord is longer than the length of a side of the inscribed equilateral triangle. One of three models can be selected with the list box:
When the experiment runs, \(I\), \(D\), \(A\), \(X\), and \(Y\) are recorded in the data table. The distribution of \(I\) is described in the distribution graph and table.