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Linenn - Jeux et Mathematiques - <br /> <b>Deprecated</b>: Non-static method plxUtils::strCheck() should not be called statically in <b>/homepages/3/d170528928/htdocs/jm/bn/core/lib/class.plx.show.php</b> on line <b>127</b><br /> Symétrie - linenn


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Symétrie

Par
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jp, le
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dimanche 13 décembre 2009 à
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23:55 |
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Vocabulaire | Page principale Jeux et Mathématiques

simetriezh

Dans le plan, la symétrie centrale est aussi le demi-tour, c'est-à-dire une rotation (trôadenn), tandis que la symétrie orthogonale est une réflexion (refleksion).
Mais la symétrie n'est pas seulement géométrique.

Let's Make a Deal!

Aux États-Unis, dans un jeu télévisé (Let's Make a Deal!), le présentateur (Monty Hall) demande au candidat de choisir entre trois portes, l'une d'entre-elles cache un superbe cadeau et il suffit de l'ouvrir pour gagner.
S'il pouvait ouvrir immédiatement la porte, le candidat aurait une chance sur trois de repartir au volant de la porsche de ses rêves et deux chances sur trois de repartir à dos d'âne.
Mais il y a une seconde étape ! Aussitôt après le premier choix du candidat, le présentateur fait ouvrir l'une des deux autres portes, une porte qui ne cache pas la voiture. Enfin, le candidat peut confirmer ou modifier son premier choix, quel dilemme, est-ce un piège ? Une chance sur trois c'était peu, est-ce pire en changeant mon choix ?

La symétrie

Si le premier choix est GAGNANT, en le modifiant on est PERDANT.
Si le premier choix est PERDANT, en le modifiant on est GAGNANT.

le résultat

Le premier choix est perdant avec la probabilité 2/3, donc en modifiant son choix, la probabilité de gagner est 2/3.

diagramme

des explications et références

Cette symétrie est celle des événements contraires (c'était mon explication du jeu), c'est-à-dire celle des ensembles complémentaires, celle que vous mettez encore en évidence en calculant les nombres de combinaisons Cnp=Cn(n-p).

                             |
                             1
                           1 | 1
                         1   2   1
                       1   3 | 3   1
                     1   4   6   4   1
                   1   5  10 |10   5   1
                 1   6  15  20  15   6   1
                             |
                             |
Détails à la page du jeu.

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