preprints.org > computer science and mathematics > probability and statistics > doi: 10.20944/preprints202410.0935.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 11 October 2024 / Approved: 11 October 2024 / Online: 14 October 2024 (05:41:55 CEST)

Critical thinking skills are important assets for scientific development. Therefore, there are many ways to enhance the critical thinking skills of students, researchers, etc., both in the field of education and scientific enterprise. In this article, we propose the practice of solving probability paradoxes and puzzles for the purpose since these problems are often complex, subtle and tricky; therefore, their solutions require many aspects of critical thinking. In the following, the Introduction outlines some of the current research on the topic without going into more details. We provide background descriptions of the paradoxes and probability paradoxes in Section 2. Section 3 provides a short description of critical thinking. We present several definitions since there is no clear consensus on one single definition, both in the literature and in the general literature. And in Section 4 current research on using puzzles for enhancing critical thinking is given. We then discuss several probability paradoxes, namely, the Monte Hall paradox, the two-envelope (exchange) paradox and the St. Petersberg paradox, in Sections 5, 6 and 7, respectively. In Section 8, a brief discussion of the statistical hypothesis testing is given emphasizing its controversial nature. We analyse these problems and concepts in such a way that critical thinking is evoked while keeping the technical details to a minimum.

Probability paradoxes and puzzles; critical thinking; solving; exercises

Computer Science and Mathematics, Probability and Statistics

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