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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
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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
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Предметный указатель
20 26-31
52
2
31
130
14-16
131
80-82
ix 107
22
12
18
12-13
2
2
19-20 158
18
151
134
vii 22 30 31 130 175
vii 22-26 130
18
39
16
22
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 r 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 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, , comparison to see
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, , comparison to see
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
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