Bertrand’s paradox (Bertrand [1]) is a problem that brings about different solutions depending on how the “random chord” is obtained. The cause of Bertrand’s paradox is known as the absence of an accurate definition of randomness (Marinoff [10]). However, according to Jaynes [7], Bertrand’s paradox is a well-posed problem with an answer of 1/2. Generally, when the subject of the geometrical probability is a point, the geometrical probability is calculated by the length of a segment or the area of a region. This method is commonly accepted without a specific explanation of randomness. In Bertrand’s paradox, however, the subject of the geometrical probability is a chord, which is part of a line, not a point. The randomness of a line is difficult to recognize intuitively, but a computer simulation demonstrates that 1/2 is the correct answer. How do we consider the randomness of a line? How do we adapt the meaning of “equiprobability” into a bunch of lines? This thesis probes the true meaning of randomness, comparing solutions of Bertrand’s paradox to that of a computer simulation and answering three questions: (1) Is randomness a result or a process? (2) What is the true subject of randomness? and (3) How should chords (lines) be counted?

Bertrand's paradox, randomness, simulation, measure of lines.