Sleeping Beauty on Monty Hall
Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Philosophies |
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| Online Access: | https://www.mdpi.com/2409-9287/5/3/15 |
| _version_ | 1827294894709800960 |
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| author | Michel Janssen Sergio Pernice |
| author_facet | Michel Janssen Sergio Pernice |
| author_sort | Michel Janssen |
| collection | DOAJ |
| description | Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful. |
| first_indexed | 2024-03-10T17:31:35Z |
| format | Article |
| id | doaj.art-5f19f27886aa454b922502247f30da9a |
| institution | Directory Open Access Journal |
| issn | 2409-9287 |
| language | English |
| last_indexed | 2024-04-24T14:11:52Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Philosophies |
| spelling | doaj.art-5f19f27886aa454b922502247f30da9a2024-04-03T09:10:28ZengMDPI AGPhilosophies2409-92872020-08-015315010.3390/philosophies5030015Sleeping Beauty on Monty HallMichel Janssen0Sergio Pernice1School of Physics and Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN 55455, USABusiness School, University of Cema, Av. Córdoba 374, Buenos Aires C1054AAP, ArgentinaInspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful.https://www.mdpi.com/2409-9287/5/3/15sleeping beauty problemmonty hall problemprobabilitybayesianfrequentist |
| spellingShingle | Michel Janssen Sergio Pernice Sleeping Beauty on Monty Hall Philosophies sleeping beauty problem monty hall problem probability bayesian frequentist |
| title | Sleeping Beauty on Monty Hall |
| title_full | Sleeping Beauty on Monty Hall |
| title_fullStr | Sleeping Beauty on Monty Hall |
| title_full_unstemmed | Sleeping Beauty on Monty Hall |
| title_short | Sleeping Beauty on Monty Hall |
| title_sort | sleeping beauty on monty hall |
| topic | sleeping beauty problem monty hall problem probability bayesian frequentist |
| url | https://www.mdpi.com/2409-9287/5/3/15 |
| work_keys_str_mv | AT micheljanssen sleepingbeautyonmontyhall AT sergiopernice sleepingbeautyonmontyhall |