• Jindřich Klůfa University of Economics, Prague
  • Nikola Kaspříková University of Economics, Prague
Keywords: Binomial distribution, entrance examinations, examples, multiple choice question tests, probability.


In this paper we shall analyze multiple choice question tests for entrance examinations from probability point of view. Multiple choice question tests are used for example for entrance examinations at Prague University of Economics, we shall analyze these tests at the Faculty of Business Administration. We shall report on probability methods, which can be used for modelling of these tests. In this case model of binomial distribution can be used for answering the following questions (under assumption of random choice of answers): what is the probability, that the number of correct answers exceeds given number, what is expected number of correct answers, etc. Results of this analysis can be used for consideration of the appropriateness of these tests.


  • Feller, W. (1970) An  Introduction to Probability Theory and its Application. New York: John Wiley.

  • Kaspříková, N. (2011) ‘Multivariate Analysis of Examination Papers’, Efficiency and Responsibility in Education 2011, Proceedings of the 8th International Conference, Prague, pp. 120–127.

  • Klůfa, J. (2011) Mathematics for entrance examinations at University of Economics, Prague: Ekopress

  • Klůfa, J. (2012) ‘Tests from probability point of view‘,  Efficiency and Responsibility in Education 2012, Proceedings of the 9th International Conference, Prague, pp. 229–233.

  • Kubanová, J., Linda, B. (2012) ‘Relation between results of the learning potential tests and study results’, Journal on Efficiency and Responsibility in Education and Science, vol. 5, no. 3, pp. 125-134.

  • Marek, L. (2012)  Pravděpodobnost, Prague: Professional Publishing

  • Premadasa, I. (1993) ‘A reappraisal of the use of multiple-choice questions’, Medical Teacher, vol. 15, no. 2-3, pp. 237-242.

  • Rao, C.R. (1973)  Linear Statistical Inference and Its Applications, New York: John Wiley

  • Rényi, A. (1972)  Teorie pravděpodobnosti. Prague:Academia.

  • Wolfram, S. (1996)  Mathematica. Addison-Wesley.

  • Zhao, Y. (2005) ‘Algorithms for converting raw scores of multiple-choice question tests to conventional percentage marks’, International Journal of Engineering Education, vol. 21, no. 6, pp. 1189-1194.

How to Cite
Klůfa, J. and Kaspříková, N. (2012) ’MULTIPLE CHOICE QUESTION TESTS FOR ENTRANCE EXAMINATIONS - A PROBABILISTIC APPROACH’, Journal on Efficiency and Responsibility in Education and Science, vol. 5, no. 4, pp. 195-202.
Research Paper