The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions.
The following table summarized known results for picking geometric objects from points in or on the boundary of other geometric objects, where 
is the Robbins constant.
See also
Bertrand's Problem, Buffon-Laplace Needle Problem, Buffon's Needle Problem, Circle Inscribing, Computational Geometry, Point Picking, Stochastic Geometry, Sylvester's Four-Point Problem
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References
Ambartzumian, R. V. (Ed.). Stochastic and Integral Geometry. Dordrecht, Netherlands: Reidel, 1987.Isaac, R. The Pleasures of Probability. New York: Springer-Verlag, 1995.Kendall, M. G. and Moran, P. A. P. Geometrical Probability. New York: Hafner, 1963.Kendall, W. S.; Barndorff-Nielson, O.; and van Lieshout, M. C. Current Trends in Stochastic Geometry: Likelihood and Computation. Boca Raton, FL: CRC Press, 1998.Klain, D. A. and Rota, G.-C. Introduction to Geometric Probability. New York: Cambridge University Press, 1997.Santaló, L. A. Introduction to Integral Geometry. Paris: Hermann, 1953.Santaló, L. A. Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976.Solomon, H. Geometric Probability. Philadelphia, PA: SIAM, 1978.Stoyan, D.; Kendall, W. S.; and Mecke, J. Stochastic Geometry and Its Applications, 2nd ed. New York: Wiley, 1987.Weisstein, E. W. "Books about Geometric Probability." http://www.ericweisstein.com/encyclopedias/books/GeometricProbability.html.
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Cite this as:
Weisstein, Eric W. "Geometric Probability." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeometricProbability.html