The monty hall problem

Document Type : Research Paper

Author

Department of Statistics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran

Abstract

In this article, the Monty Hall problem is explored as one of the puzzles in the realm of probability theory. The mathematical proof of this problem is based on two fundamental principles of probability theory: the law of total probability and Bayes' theorem. The first and last mathematical proofs presented for this problem are introduced. The Gilman games are also reviewed in connection with this problem. Finally, applications of this problem in philosophy, physics, economics, and psychology are discussed.

Keywords

References

[1] P. Baumann, Single-case probabilities and the case of Monty Hall: Levy’s View, syntheses, 162 (2008) 265–273.
[2] A. L. Bello, Ask Marilyn: the mathematical controversy in Parade Magazine, Parade (1990) 275–276.
[3] A. Ben-Naim, Discover Probability, World Scientific, New Jersey, (2015).
[4] B. Burnsand and M. Wieth, The collider principle in casual reasoning: why the Monty Hall Problem is so hard, Journal of experimental psychology, 103 (2004) 436–449.
[5] G. M. D’Arioano, R. D. Gill, M. Keyl, R. F. Werner, B. Kummer and H. Maassen, The quantum Monty Hall problem, Quantum information and computation, 2 (2002) 355–366.
[6] A. B. Francisco, Coutinho, Eduardo, Massad, CMath FIMA and Luiz, N. Oliveira, Monty Hall problem revisited once more, Mathematics TODAY, (2019) 24–26.
[7] L. Gillman, The car and goats, Focus (MAA newsletter), 11(3) (1991) p. 8.
[8] L. Gillman, The car and the goats, Amrican Mathematical Monthly, 99(1) (1992) 3–7.
[9] R. Isaac, The Pleasures of Probability, Springer, Berlin (1995).
[10] S. J. Miller, The Probability Lifesaver, Princeton University Press, Princeton and Oxford (2017).
[11] J. Rosenhouse, The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser. Oxford University Press, Inc., New York, New York (2009).
[12] A. Tor and M. Bazerman, Focusing failures in competitive environments: explaining decision errors in the Monty Hall game, the acquiring a company problem, and multiparty ultimatums, Journal of behavioral decision making, 16 (2003) 353–374.
[13] M. vos Savant, Ask Marilyn, Parade, (1990, 9 Sept) p. 22.
[14] M. vos Savant, Ask Marilyn, Parade, (1990, 9 Dec) p. 26.
[15] vos Savant, M. Ask Marilyn, Parade, (1991, 7 Jul) 26–29.
Mathematics and Society
Volume 4, Issue 3 - Serial Number 3
September 2019
Pages 61-71

Files

History

  • Receive Date: 20 November 2019
  • Revise Date: 28 June 2020
  • Accept Date: 03 July 2020
  • Publish Date: 22 November 2019

Share

How to cite

Statistics