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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 TeaserАвтор: 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?
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2009Количество страниц: 207Добавлена в каталог: 08.02.2014Операции: Положить на полку |
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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 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 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, 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, 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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