Classic Problems of Probability

328 Pages·2012·7.16 MB·English

by  Prakash Gorroochurn

Classic Problems
of Probability

Classic Problems
of Probability
Prakash Gorroochurn
DepartmentofBiostatistics,ColumbiaUniversity,NewYork,NY
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Gorroochurn,Prakash,1971-
Classicproblemsofprobability/PrakashGorroochurn.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-118-06325-5(pbk.)
1. Probabilities–Famousproblems.2. Probabilities–History.I.Title.
QA273.A4G672012
519.2–dc23
2011051089
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
To Nishi and Premal
operae pretium est
Contents
Preface ix
Acknowledgments xi
1 CardanoandGamesofChance(1564) 1
2 GalileoandaDiscoveryConcerningDice(1620) 9
3 TheChevalierdeM(cid:1)er(cid:1)eProblemI:TheProblemofDice(1654) 13
4 TheChevalierdeM(cid:1)er(cid:1)eProblemII:TheProblemofPoints(1654) 20
5 HuygensandtheGambler’sRuin(1657) 39
6 ThePepys–NewtonConnection(1693) 49
7 RencontreswithMontmort(1708) 54
8 JacobBernoulliandhisGoldenTheorem(1713) 62
9 DeMoivre’sProblem(1730) 81
10 DeMoivre,Gauss,andtheNormalCurve(1730,1809) 89
11 DanielBernoulliandtheSt.PetersburgProblem(1738) 108
12 d’Alembertandthe“CroixouPile”Article(1754) 119
13 d’AlembertandtheGambler’sFallacy(1761) 124
14 Bayes,Laplace,andPhilosophiesofProbability(1764,1774) 129
15 Leibniz’sError(1768) 156
16 TheBuffonNeedleProblem(1777) 159
vii
viii Contents
17 Bertrand’sBallotProblem(1887) 169
18 Bertrand’sStrangeThreeBoxes(1889) 175
19 Bertrand’sChords(1889) 179
20 ThreeCoinsandaPuzzlefromGalton(1894) 186
21 LewisCarroll’sPillowProblemNo.72(1894) 189
22 BorelandaDifferentKindofNormality(1909) 194
23 Borel’sParadoxandKolmogorov’sAxioms(1909,1933) 199
24 OfBorel,Monkeys,andtheNewCreationism(1913) 208
25 Kraitchik’sNecktiesandNewcomb’sProblem(1930,1960) 215
26 FisherandtheLadyTastingTea(1935) 224
27 BenfordandthePeculiarBehavioroftheFirstSignificantDigit(1938) 233
28 CoincidingBirthdays(1939) 240
29 L(cid:1)evyandtheArcSineLaw(1939) 247
30 Simpson’sParadox(1951) 253
31 Gamow,Stern,andElevators(1958) 260
32 Monty-Hall,Cars,andGoats(1975) 264
33 Parrondo’sPerplexingParadox(1996) 271
Bibliography 277
Photo Credits 296
Index 299