In this chapter, we explore several problems in geometric probability. These problems are interesting, conceptually clear, and the analysis is relatively simple. Thus, they are good problems for the student of probability. In addition, Buffon's problems and Bertrand's problem are historically famous, and contributed significantly to the early development of probability theory.
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10.1: Buffon's Problems
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Buffon's experiments are very old and famous random experiments, named after comte de Buffon. These experiments are considered to be among the first problems in geometric probability.
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10.2: Bertrand's Paradox
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Bertrand's problem is to find the probability that a random chord on a circle will be longer than the length of a side of the inscribed equilateral triangle. The problem is named after the French mathematician Joseph Louis Bertrand, who studied the problem in 1889.
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10.3: Random Triangles
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Suppose that a stick is randomly broken in two places. What is the probability that the three pieces form a triangle?