id: 06310357
dt: a
an: 2014d.00787
au: Borovcnik, Manfred; Kapadia, Ramesh
ti: From puzzles and paradoxes to concepts in probability.
so: Chernoff, Egan J. (ed.) et al., Probabilistic thinking. Presenting plural
perspectives. Dordrecht: Springer (ISBN 978-94-007-7154-3/hbk;
978-94-007-7155-0/ebook). Advances in Mathematics Education, 35-73
(2014).
py: 2014
pu: Dordrecht: Springer
la: EN
cc: K50 K60 E20
ut: division of stakes; expectation; independence; relative frequencies;
subjective (personal) probability; conditional probability; axiomatic
probability; random samples; fundamental ideas; d’Alembert; Bayes;
Bernoulli; Bertrand; Çinlar; Falk; de Finetti; Huygens; Kolmogorov;
von Mises; Székely
ci:
li: doi:10.1007/978-94-007-7155-0_3
ab: 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.
rv: