{"id":1083,"date":"2011-08-16T10:34:33","date_gmt":"2011-08-16T10:34:33","guid":{"rendered":"http:\/\/www.navision-blog.de\/2011\/08\/16\/some-special-monads-in-f-part-4-of-n-application-the-monty-hall-problem\/"},"modified":"2022-11-20T13:45:36","modified_gmt":"2022-11-20T13:45:36","slug":"some-special-monads-in-f-part-4-of-n-application-the-monty-hall-problem","status":"publish","type":"post","link":"http:\/\/www.navision-blog.de\/blog\/2011\/08\/16\/some-special-monads-in-f-part-4-of-n-application-the-monty-hall-problem\/","title":{"rendered":"Some special monads in F# – Part 4 of n – Application: The Monty Hall problem"},"content":{"rendered":"

In the last part of this blog series<\/a> I showed a DistributionMonad, which allows to perform queries to probability scenarios. Today we will use this monad in order to solve the famous Monty Hall problem<\/a>. This article is based on the excellent paper by Martin Erwig and Steve Kollmansberger called "Functional Pearls: Probabilistic functional programming in Haskell"<\/a>.<\/p>\n

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\u201cSuppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?\u201d<\/p>\n

[problem definition from Wikipedia<\/a>]<\/p>\n<\/blockquote>\n

Let\u2019s start by modeling the first choice using the DistributionMonad:<\/p>\n