3 ms·

Vos Savant originally posed the problem with ambiguous wording.

• mcphage 12y ago
  The original problem, from her website: "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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? Craig F. Whitaker Columbia, Maryland" (a) she didn't originally pose the problem, it was a question asked of her, and (b) the wording of the problem is not ambiguous.
  • bztzt 12y ago
    the ambiguity is that it's presented as something the host does in this particular instance, but the validity of the probability calculations depends on it being a protocol the host always follows (in particular, that the host will always reveal one of the goats not behind the contestant's first choice of doors).
    • mcphage 12y ago
      There is no "always follows". This is an event which will not be repeated in the history of the world. All there is is 3 doors: you pick one, the host opens another door which contains a goat, and offers you a choice. Why he picked the door that he chose is irrelevant. All that is relevant is that (a) it's not the door you chose, and (b) it contains a goat. You don't need anything beyond that to solve this problem. If you think you need something beyond that to solve the problem, you're not solving it correctly.
      • PalmerEldritch 12y ago
        "Why he picked the door that he chose is irrelevant" I disagree. If he picked the door at random and it just happened to contain a goat it's 50/50. If he picked the door because he was always going to pick that door if it contained a goat then it's 50/50