
06310357
a
2014d.00787
Borovcnik, Manfred
Kapadia, Ramesh
From puzzles and paradoxes to concepts in probability.
Chernoff, Egan J. (ed.) et al., Probabilistic thinking. Presenting plural perspectives. Dordrecht: Springer (ISBN 9789400771543/hbk; 9789400771550/ebook). Advances in Mathematics Education, 3573 (2014).
2014
Dordrecht: Springer
EN
K50
K60
E20
division of stakes
expectation
independence
relative frequencies
subjective (personal) probability
conditional probability
axiomatic probability
random samples
fundamental ideas
d'Alembert
Bayes
Bernoulli
Bertrand
\c{C}inlar
Falk
de Finetti
Huygens
Kolmogorov
von Mises
Sz\'ekely
doi:10.1007/9789400771550_3
Summary: This chapter focuses on how puzzles and paradoxes in probability developed into mathematical concepts. After an introduction to background ideas, we present each paradox, discuss why it is paradoxical, and give a normative solution as well as links to further ideas and teaching; a similar approach is taken to puzzles. After discussing the role of paradoxes, the paradoxes are grouped in topics: equal likelihood, expectation, relative frequencies, and personal probabilities. These cover the usual approaches of the a priori theory (APT), the frequentist theory (FQT), and the subjectivist theory (SJT). From our discussion it should become clear that a restriction to only one philosophical position towards probability  either objectivist or subjectivist  restricts understanding and fails to develop good applications. A section on the central mathematical ideas of probability is included to give an overview for educators to plan a coherent and consistent probability curriculum and conclusions are drawn.