Global Data Science Forum

The Monty Hall Problem

By Moloy De posted 13 days ago

In Data Science we help client to decide between their options. Monty hall is a decision making problem using conditional probability. For popular study one may refer to the Monty Hall Problem in Wikipedia. It uses Conditional Probability for making the choice.



Vos Savant's response was that the contestant should switch to the other door.

The given probabilities depend on specific 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. Yet another insight is that your chance of winning by switching doors is directly related to your chance of choosing the winning door in the first place: if you choose the correct door on your first try, then switching loses; if you choose a wrong door on your first try, then switching wins; your chance of choosing the correct door on your first try is 1/3, and the chance of choosing a wrong door is 2/3.


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.

Question I: Could we generalize the game to n doors and 1 goat?

Question II: Could we generalize the game to n doors and k goats, k < n?