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Rosenhouse J. — The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser
Rosenhouse J. — The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser

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Название: The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser

Автор: Rosenhouse J.

Аннотация:

"Let's Make a Deal," with its popular host Monty Hall, was a staple of 1970s game shows, with squirming contestants trying to guess which of three doors concealed the grand prize. The contestant chooses a door, but does not open it. Monty opens a different door, always empty. The contestant faces a choice: stick with his original door or switch to the remaining door?

This mindbender is known as "the Monty Hall Problem," the subject of Jason Rosenhouse's witty new book. Rosenhouse, associate professor of mathematics at James Madison University, examines the problem from multiple angles, lucidly explaining why, though counterintuitive, the best choice is to switch doors.

//The Monty Hall Problem// is sure to elicit emotional responses — as the conundrum itself has for years among mathematicians, philosophers, physicists, and others. Rosenhouse acknowledges the provocative nature of the problem and faces it head on, thoroughly and convincingly explaining the math and logic of the problem and addressing several variations.

Although Rosenhouse's enthusiasm for the subject is infectious, readers whose education ended with Math 101 may find much of this book beyond reach, as it is thick with equations. But for those who aren't arithmophobes, //The Monty Hall Problem// is delightfully challenging.

Reviewed by Kelli Christiansen


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2009

Количество страниц: 207

Добавлена в каталог: 08.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$American\quad Statistician$      20 26-31
$Art\quad of\quad Conjecturing,\quad The$      52
$Beautiful\quad Mind,\quad A$      2
$Bostonia$      31
$Bridge\quadToday$      130
$Calcul\quaddes\quadProbabilite$      14-16
$Curious\quad Incident\quad of \quadthe\quad Dog\quad in\quad the\quad Night-time,\quad The$      131
$Deal\quad or\quad No\quad Deal$      80-82
$e$      ix 107
$Economic\quad Perspectives$      22
$Emergence\quad of\quad Probability,\quad The$      12
$Fifty\quad Challenging\quad Problems\quad in\quad Probability\quad with\quad Solutions$      18
$Games,\quad Gods\quad and\quad Gambling$      12-13
$Good\quad Will\quad Hunting$      2
$Jurassic\quad Park$      2
$Let’s\quad Make\quad a\quad Deal$      19-20 158
$Mathematical\quad Ideas\quad in\quad Biology$      18
$Mind’s\quad Arrows,\quad The$      151
$Neuropharmacology$      134
$New\quad York\quad Times$      vii 22 30 31 130 175
$Parade$      vii 22-26 130
$Paradoxicon,\quad The$      18
$Riddle\quad of\quad Scheherazade\quad and\quad Other\quad Amazing\quad Puzzles,\quad The$      39
$Scientific\quad American$      16
$Stand,\quad The$      22
$Torn\quad Curtain$      2
Aaron, E.      149 151
Actual probability      50-51 64 85
Agassi, Andre      22
AirPort      71
Algebra      119-20
Algorithms      149
Alonso, D.      152
Amsterdam      8
Architecture, cognitive      145
Armies of indifference      40
artificial intelligence      128
Asperger’s syndrome      131
Athens      8
Autism      131
Average      118-19 125 162
Axioms      85
Baggage retrieval carousel      71 85
Bapeswara Rao, V. V.      89
Bar — Hillel, Maya      137-38 140 143-45
base case      8 72;
Base rate fallacy      8
battery      151
Bayes, Thomas      12-14
Bayesian interpretation of probability      165-74; see Probability theory interpretations Peter
Bayes’ Theorem, alternatives to      22
Bayes’ Theorem, baggage carousel problem and      71-72
Bayes’ Theorem, doctors and      177
Bayes’ Theorem, nonrandom car placement and      78-80
Bayes’ Theorem, posterior probability and      70 95 139 141 152 171-72
Bayes’ Theorem, prior probability and      13 70 81 88 95 141 152
Bayes’ Theorem, progressive MHP and      92-94 97 108
Bayes’ Theorem, proportionality principle and      83
Bayes’ Theorem, solving MHP variations with      vii ix 37 73-75 79-80 141 142 169
Bayes’ Theorem, statement of and basic facts about      69-73
Bayes’ Theorem, two-host problem and      117
Bayes’ Theorem, understanding technical details of      137
Bayes’ Theorem, unreliable Monty and      77-78
Bedient, Richard      19
Berlin      8
Bernoulli, Jakob      52 86
Bertrand Box Paradox      14-16 44 69
Bertrand, Joseph      14-16 40
Bibiloni, L.      112
Binomial coefficients      11
Birth order      138-39
Birthday problem      5-7
bookkeeping      122
Brain      134
Brainteasers      12 14 32 134 147
Brazil      146
Bridge (card game)      33 128-31
Brown, Thad      41 134-35
Burns, Bruce      135 151
Bush, George H. W.      22
Calculus      2 110 148
Candy      175-76
Capriciousness      41
Cardano, G.      10
Cartesian product      59
Casino games      86
Central Intelligence Agency      31
Certainty, intrinsic      144
Chaganty, N. R.      29-31
Chen, M. Keith      175-16
Chen, Serena      42 136
Chess      128
Chevalier de M$\acute{e}$r$\acute{e}$      10
China      146
Christmas      6
Chump, feeling like a      41
Cigarette      71
Classical probability      43
Coding      104
Cognitive factors      152
Cognitive illusion      146
Cognitive scientists      viii 8 31 87 128 133 153
coin tossing      10 13 16 42-43 45 51 58 60 66-68 84 86 88 122
Coin — Toss Monty      116-18
Collider principle      see Monty Hall problem collider
Communications channel      105
Computer      126 135
Computer scientists      177
Conditional probability      vii ix 13-14 21 63-66 69-70 77 91 98 102 119-20 137 139 142 145 152 171
Consequence, negative      136-137
Correlation, inverse      104 126
Correlations, statistical      158 161-62
Counterfactual      41 136 173
Craine, Timothy      118 120-21
Crowe, Russell      2
Dahiya, R. C.      29-31
Damon, Matt      2
databases      133
David, F. N.      12-13
Dawkins, Richard      23
De Beys, W.      152
Decision theory/theorists      42 87 134 177
deck of cards      4-5 42-43 46 53 60 127
Declarer      129
Degree of belief/confidence      13 85-88
Denominator      43
Dental cavities      71
Derks, P. L.      152
Diaconis, Persi      22-23
Dice Rolling      42-45 58 61 68
digit      126
Disciplines, academic      133
Discrete random variable      136 175-76;
DNA      14
Doe, Samuel      22
Dougherty, M. R. R      152
Doviak, M. J.      29-31
Dummy (in bridge)      129
d’Alembert, Jean le Rond      15 44
Earth      36
Ecological Intelligence      149
Economists      viii 31 133 137
Educators      177
Elementary arithmetic      1
Elementary physics      84
Empirical probability      169
Engel, E.      112
Entanglement      127-128
Epistemic probability      see Probability theory epistemic
Epistemic statistical probability      see Probability theory epistemic
Equiprobable      38 68 86 93-94 96 100 138
Erd$\ddot{o}$s, Paul      54-55
Euclid      85
Expectation/expected value      121-26 162
Eye Movement Responses of Heroin Addicts and Controls During Word and Object Recognition      133
Falk, Ruma      18 137-38 140 143-45
Falletta, Nicholas      18-19
False negatives/positives      7-8 72 163
Favorable outcomes      43-44 85-86
Fermat, Pierre de      9-12
Final examination      155
fingerprints      70
Five-card suit      130
Formalism, mathematical      140
Fox, Craig      152
FRACTION      120
Franco — Watkins, A. M.      152
Frequentist probability, interpretations of probability and      see Probability theory interpretations
Frequentist probability, long-runs and      10 50 85-86 121 158 161-63
Frequentist probability, naturalness of      87
Frequentist probability, reference classes and      8-9 87
Friedman, D.      152
Fuel tank      151
Function      85
Galileo, G.      10
gambling      10 85
Game show      2 32-33 35 80 130 133-34 147
Game theory      177
Gardner, Martin      16-18 147
Gauntlet      158
Generalization      126
Geneticists      177
Geometry      85
Georges, John      118 120-21
Gigerenzer, G.      149-50
Gilovich, Thomas      42 136
Glymour, Clark      151
Goldblum, Jeff      2
Gorbachev, Mikhail      22
Granberg, Donald      41 134-35 146-7
Grief, five stages of      5
Gut instinct      41
Hacking, Ian      12-13
Haddon, Mark      131
Hall, R. J.      134
Hand waving      167
Heroin addiction      133
Hitchcock, Alfred      2
Horgan, Terence      164 174
Human decision making      viii 31-32
Human psychology      42 146
Human self-esteem      147
Ideal reasoner      88
Identical twins      6
Ijikawa, S.      141-145 148
Illusion, cognitive      110; see Cognitive illusion increasing function
Induction      ix 93-94 103
Infinite series      107
Information formats      149
Information theory      104-5 126-28
Initial choice      37 39 47 73 79 89 100 114 116 118 123 130 161
Integration by parts      148
Internet, the      133
Interpretations of probability      59 66; interpretations
Intuition      79 89 98 100-101 128 140 150 167
Intuitions, primary and secondary      144-45
Inverse probability      22
Iraq      22
Journalist      vii 155
Journals, mathematics and statistics      133
Juries      177
King, Stephen      22
Krantz, Steven      54
Krauss, Stefan      152
Kuwait      22
Laplace, Pierre — Simon      12-13
Law of alternatives      66
Law of Large Numbers      51 85-86
Law of total probability      65-66 68-69 73-74 94 97 106
Law professors      177
leap years      6
Leibniz, G.      16
Levav, J.      152
Level of ignorance      84
Levy, Ken      165-67
Liberia      22
Likelihood      70 159
Likelihood principle      145
Limiting frequencies      85
Logic      36 38 48 66 83 85 170 177
Long-runs      25; see Frequentist probability long-runs
Lung cancer      71 87
Manuscript      175
Martin, Phil      33 128 130
Massachusetts Institute of Technology      31
Mathematical model      41 44 46 49-50 60 141
Mathematician      viii 1 10 24 26 28 30 43 55 70 84 140 148 175
Mathematics classes      43 105 148
Maxwell, James Clerk      2
Mean value theorem      2
Medical testing      7-8 72 163
Medvec, Victoria      42 136
Melodrama      32
MHD-gnostic/agnostic condition      41
Middle Ages      10
Milan      8
Monte Carlo methods/simulations      25 49-54 85-86 169
Monty Hall      2 19-22 158 166 172
Monty Hall Dilemma, The      134
Monty Hall Problem, $Deal\quad or\quad No\quad Deal$, comparison to      see $Deal\quad or\quad No\quad Deal$
Monty Hall Problem, bridge and      see Bridge
Monty Hall Problem, causal structure and      152 158 162
Monty Hall Problem, collider principle and      151-52
Monty Hall Problem, computer simulations of      49-52
Monty Hall Problem, conditional vs. unconditional forms of      29 157
Monty Hall Problem, cross-cultural comparisons of      146-47
Monty Hall Problem, emotional considerations and      137
Monty Hall Problem, frequentist vs. probabilistic statements of      149-51
Monty Hall Problem, immunity to higher education and      31
Monty Hall Problem, multiple-door versions of      118-21
Monty Hall Problem, multiple-prize versions of      123-26
Monty Hall Problem, progressive version of      see progressive Monty Hall problem
Monty Hall Problem, quantum mechanical versions of      see Quantum mechanics Monty
Monty Hall Problem, sample space for      46-47 61-63
Monty Hall Problem, sloppy and careless formulations of      160
Monty Hall Problem, statement of      vii 2 35
Monty Hall Problem, studies of people’s reactions to      135
Monty Hall Problem, three-door versions, general principles for      116 156
Monty Hall Problem, three-player version of      116
Monty Hall Problem, two-host version of      116-18
Monty Hall Problem, two-player versions of      115-16 165-70
Monty Hall Problem, vertigo and      138
Monty Hall trap      130
Monty, R. A.      133
Monty’s selection procedure, $Deal\quad or\quad No\quad Deal$, comparison to      see $Deal\quad or\quad No\quad Deal$
Monty’s selection procedure, always opens lowest/highest door      75 83
Monty’s selection procedure, benevolent/malevolent behaviors and      113-14
Monty’s selection procedure, biases in      114
Monty’s selection procedure, nonzero probability of revealing car      57-58
Monty’s selection procedure, providing no reason for altering prior Monty’s selection procedure, probability      79
Monty’s selection procedure, relevance of      3 25 27 37 48 62 64 74 113 130 156 160
Monty’s selection procedure, reveals a goat with probability p      119-21
Moon, the      36
Morgan, J. P.      29-31
Moser, Paul      157-65 174
Mosteller, Fred      18
Motorcycles      123-24
Mulder, D. Hudson      157-65 174
Multiple-door argument      37-38
Nalebuff, Barry      22
1 2
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