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The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
This question is called the Monty Hall problem due to its resembling scenarios on the game show Let's Make a Deal, hosted by Monty Hall. It was a known logic problem before it was used in "Ask Marilyn". She said the selection should be switched to door #2 because it has a 2 ⁄ 3 probability of success, while door #1 has just 1 ⁄ 3.
In the late summer of 2006, an interactive DVD version of Let's Make a Deal was released by Imagination Games, which also features classic clips from the Monty Hall years of the show. In 2010, Pressman Toy Corporation released an updated version of the box game, with gameplay more similar to the 1974 version, featuring Brady on the box cover.
Monty Hall OC, OM (born Monte Halparin; August 25, 1921 – September 30, 2017) was a Canadian-American [1] [2] radio and television show host who moved to the United States in 1955 to pursue a career in broadcasting. After working as a radio newsreader and sportscaster, Hall returned to television in the U.S., this time in game shows.
Either Monty Hall opens the second door and reveals a goat, in which case the contestant should switch to the last remaining door, or else Monty Hall opens a door and reveals the car, in which case the contestant should obviously switch to that door.--Lorenzo Traldi 10:41, 20 December 2006 (UTC)
From this tree it's clear if you've picked door 1 and the host has opened door 3, the probability the car is behind door 2 is twice the probability the car is behind door 1 (because the host must open door 3 if the car is behind door 2, but opens either door 2 or door 3 - presumably each one half the time - if the car is behind door 1).
When Monty opens his doors, it reduces the number of doors down to 2, which is what produces the illusion: people think that the probability of the car must correspond to the current number of doors, and thus be 1/2, instead of corresponding to the number of ways of getting to that 2-door situation, which is what makes it 1/n.
The conditional probability the car is behind Door 2 given the player has picked Door 1 and has seen the host opens Door 3 is defined as the probability the car is behind Door 2 in the cases the host opens Door 3 (1/3) divided by the probability of all cases where the host opens Door 3 (1/2), therefore the conditional probability is (1/3)/(1/2 ...