Clarifying the Language of Chance Using Basic Conditional Probability Reasoning: The Monty Hall Problem
Author(s)
Pejmon Sadri
ABSTRACT
Clarity and preciseness in the use of language is crucial when communicating mathematical and probabilistic ideas. Lack of these can make even the simplest problem difficult to understand and solve. One such problem is the Monty Hall problem. In the past, a controversy was stirred among professional mathematicians when trying to reach a consensus on a solution to the problem. The problem still creates confusion among some of those who are asked to solve it for the first time. We purport to demonstrate the use of more precise language of basic conditional probability could have prevented the controversy.
Clarity and preciseness in the use of language is crucial when communicating mathematical and probabilistic ideas. Lack of these can make even the simplest problem difficult to understand and solve. One such problem is the Monty Hall problem. In the past, a controversy was stirred among professional mathematicians when trying to reach a consensus on a solution to the problem. The problem still creates confusion among some of those who are asked to solve it for the first time. We purport to demonstrate the use of more precise language of basic conditional probability could have prevented the controversy.
Cite this paper
P. Sadri, "Clarifying the Language of Chance Using Basic Conditional Probability Reasoning: The Monty Hall Problem," Open Journal of Discrete Mathematics, Vol. 2 No. 4, 2012, pp. 164-168. doi: 10.4236/ojdm.2012.24033.
P. Sadri, "Clarifying the Language of Chance Using Basic Conditional Probability Reasoning: The Monty Hall Problem," Open Journal of Discrete Mathematics, Vol. 2 No. 4, 2012, pp. 164-168. doi: 10.4236/ojdm.2012.24033.
References
[1] J. Mestre, “Hispanic and Anglo Students’ Misconceptions in Mathematics,” ERIC Digest, 1989. [2] K. Abouchedid and R. Nasser, “The Role of Presentation and Response Format in Understanding, Preconceptions and Alternative Concepts in Algebra Problems,” Notre Dame University, Lebanon, 2000. [3] L. Wittgenstein, “Remarks on the Foundations of Mathematics,” Revised Edition, MIT Press, Cambridge, 1983. [4] E. Barbean, “Fallacies, Flaws, and Flimflam,” The College Mathematics Journal, Vol. 24, No. 2, 1993, pp. 149-154. [5] C. M. Grinstead and J. L. Snell, “Introduction to Probability,” 2nd Edition, American Mathematical Society, Providence, 1998. [6] M. vos Savant, “Ask Marilyn Column,” Parade Magazine, September 2, 1990, p. 14. [7] M. vos Savant, “Ask Marilyn Column,” Parade Magazine, December 2, 1990, p. 28. [8] American College of Physicians—American Society of Internal Medicine, “Compendium of Primers,” Effective Clinical Practice, Vol. 3, No. 3, 2000, p. 2. [9] M. Hilger, “Texas Hold’em Odds and Probabilities: Limit, No Limit, and Tournament Strategies,” 1st Edition, Dimat Enterprises, Inc., Duluth, 2006. [10] C. Darwin, “On the Origin of Species, the Illustrated Edition,” Sterling Publishing, New York, 2008. [11] M. Born, “Physics in My Generation,” Springer-Verlag, New York, 1969. [12] B. Greene, “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory,” W. W. Norton & Company, New York, 2003.
[1] J. Mestre, “Hispanic and Anglo Students’ Misconceptions in Mathematics,” ERIC Digest, 1989. [2] K. Abouchedid and R. Nasser, “The Role of Presentation and Response Format in Understanding, Preconceptions and Alternative Concepts in Algebra Problems,” Notre Dame University, Lebanon, 2000. [3] L. Wittgenstein, “Remarks on the Foundations of Mathematics,” Revised Edition, MIT Press, Cambridge, 1983. [4] E. Barbean, “Fallacies, Flaws, and Flimflam,” The College Mathematics Journal, Vol. 24, No. 2, 1993, pp. 149-154. [5] C. M. Grinstead and J. L. Snell, “Introduction to Probability,” 2nd Edition, American Mathematical Society, Providence, 1998. [6] M. vos Savant, “Ask Marilyn Column,” Parade Magazine, September 2, 1990, p. 14. [7] M. vos Savant, “Ask Marilyn Column,” Parade Magazine, December 2, 1990, p. 28. [8] American College of Physicians—American Society of Internal Medicine, “Compendium of Primers,” Effective Clinical Practice, Vol. 3, No. 3, 2000, p. 2. [9] M. Hilger, “Texas Hold’em Odds and Probabilities: Limit, No Limit, and Tournament Strategies,” 1st Edition, Dimat Enterprises, Inc., Duluth, 2006. [10] C. Darwin, “On the Origin of Species, the Illustrated Edition,” Sterling Publishing, New York, 2008. [11] M. Born, “Physics in My Generation,” Springer-Verlag, New York, 1969. [12] B. Greene, “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory,” W. W. Norton & Company, New York, 2003.