Original sentence: "As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter.Although not stated in this version, a solution is often based on the additional assumptions that the car is initially equally likely to be behind each door and that the host must open a door showing a goat, must (completely) randomly (i.Other interpretations of the problem have been discussed in mathematical literature where the conditional probability of winning by switching, given the door first chosen and the door opened by the host, can be anything from 0 to 1.The Monty Hall problem, in its most detailed interpretation, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox.with equal probabilties) choose which door to open if both hide goats, and must make the offer to switch
Edited sentence: Although not explicitly stated in this version, the solution is usually based on the additional assumptions that the car is initially equally likely to be behind each door and that the host must open a door showing a goat, must randomly choose which door to open if both hide goats, and must make the offer to switch.As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter.Other interpretations of the problem have been discussed in mathematical literature where the probability of winning by switching can be anything from 0 to 1.The Monty Hall problem, in its usual interpretation, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox