How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?

Bongju Lee; Yong Sik Yun

doi:10.29333/ejmste/86163

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Bongju Lee ¹, Yong Sik Yun ² ^*

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¹ Kyungpook National University, Daegu, SOUTH KOREA² Jeju National University, Jeju, SOUTH KOREA^* Corresponding Author

Abstract

The concept of probability has a unique characteristic that causes confusion when a sample space is not clearly defined. This inherent nature of probability has been demonstrated in Bertrand’s chord problem, which is well-known as the paradox of probability theory. This study demonstrated that a single probability in Bertrand’s chord problem can be obtained by modifying it to clearly redescribe its sample space, and examined that how college students clarify the sample space. To this end, five modified questions were formed using Bertrand’s chord problem to ensure that the sample space of each question was clearly expressed and were used to develop a survey questionnaire. The participants of the survey were 68 college students studying mathematics or mathematics education. The results of this study demonstrated that many college students have difficulty to seek out the sample spaces in some probability problems. Thus we suggested the importance of emphasizing to clarify the sample space in probability education.

Keywords

Bertrand’s chord problem
paradox
college students
five modified Bertrand’s questions
probability
sample space

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 14, Issue 6, June 2018, 2067-2079

https://doi.org/10.29333/ejmste/86163

Publication date: 02 Mar 2018

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How to cite this article

APA

Lee, B., & Yun, Y. S. (2018). How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?. Eurasia Journal of Mathematics, Science and Technology Education, 14(6), 2067-2079. https://doi.org/10.29333/ejmste/86163

Vancouver

Lee B, Yun YS. How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?. EURASIA J Math Sci Tech Ed. 2018;14(6):2067-79. https://doi.org/10.29333/ejmste/86163

AMA

Lee B, Yun YS. How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?. EURASIA J Math Sci Tech Ed. 2018;14(6), 2067-2079. https://doi.org/10.29333/ejmste/86163

Chicago

Lee, Bongju, and Yong Sik Yun. "How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 6 (2018): 2067-2079. https://doi.org/10.29333/ejmste/86163

Harvard

Lee, B., and Yun, Y. S. (2018). How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?. Eurasia Journal of Mathematics, Science and Technology Education, 14(6), pp. 2067-2079. https://doi.org/10.29333/ejmste/86163

MLA

Lee, Bongju et al. "How do College Students Clarify Five Sample Spaces for Bertrand’s Chord Problem?". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 6, 2018, pp. 2067-2079. https://doi.org/10.29333/ejmste/86163