Investigating and Expanding the Monty Hall Problem - amazonia.fiocruz.br

Investigating and Expanding the Monty Hall Problem - amusing phrase

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Investigating and Expanding the Monty Hall Problem Video

Excel VBA Simulation: Can We Solve The Monty Hall Problem? #4

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed and solved in a letter by Steve Selvin to the American Statistician in Suppose 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.

He then says to Investigating and Expanding the Monty Hall Problem, "Do you want to pick door No. Vos Savant's response was that the contestant should switch to the other door. The given probabilities depend on aand assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 than was available at the beginning of the game when door 1 was chosen by the player: the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities.

Many readers of Vos Savant's Invesrigating refused to believe switching is beneficial despite her explanation.

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After the problem appeared in Paradeapproximately 10, readers, including nearly 1, with PhDswrote to the magazine, most of them claiming vos Expxnding was wrong. The problem is a paradox of the veridical type, because the correct choice that one should switch doors is so counterintuitive it can seem absurd, but is nevertheless demonstrably true.

The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox. Steve Selvin wrote a letter to the American Statistician in describing a problem based on the game show Let's Make a Deal Expandiing, [1] dubbing it the "Monty Hall problem" in a subsequent letter.

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The key to this solution is the behavior of the host. Ambiguities in the Parade version do not explicitly define the protocol of the Expandig. However, Marilyn vos Savant's solution [3] printed alongside Whitaker's question implies, and both Selven [1] and Savant [5] explicitly define, the role of the host as follows:.

When any of these assumptions is varied, it can change the probability of winning by switching doors as detailed in the section below.

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It is also typically presumed that the car is initially hidden randomly behind the doors and that, if the player initially picks the car, Exanding the host's choice of which goat-hiding door to open is random. The solution presented by vos Savant in Parade shows the three possible arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case: [12]. A player who stays with the initial choice wins in only one out of three of these equally likely possibilities, while a player who switches wins in two out of three.

An intuitive explanation is that, if the contestant initially picks a goat 2 of 3 doorsthe contestant will win the car by switching because the other Gender Literature can no longer be picked, whereas if the contestant initially picks the car 1 of 3 doorsthe contestant will not win the car by switching. This would be true if the host opens a door randomly, but that is not the case; the door opened depends on the player's initial Pdoblem, so the assumption of independence does not hold.

These are the only cases where the host opens door 3, so if the player has picked door 1 and the host opens door 3 the car is twice as likely to be behind door 2. The key is that if the car is behind door 2 the host must open door 3, but if the car is behind door 1 the host can open either door.

Another way Inveztigating understand the solution is to consider the two original unchosen doors together. So the player's choice after the host opens a door is no different than if the host offered the player the option to switch from Investigating and Expanding the Monty Hall Problem original chosen door to the set of both remaining doors.]