5 ms·

I read about this problem and the fact that multiple educated writers falsely called out vos Savant in an old Martin Gardner column, and it shines in my memory

I read about this problem and the fact that multiple educated writers falsely called out vos Savant in an old Martin Gardner column, and it shines in my memory as one of the problems that illuminated math for me and made me see recreational math as worthwhile. Of course back when he wrote about it the topic of sexism was mercifully left out, and I honestly hadn't given a moment's thought to the fact that vos Savant was a woman until I read this new take on it, but there you go. Have standards for what makes something confusing and difficult to understand risen significantly over the decades? When I brought this problem up with my group of (admittedly geeky and mathy) friends no one was left unconvinced by the end of the afternoon, and most even had the intuition as well as the mathematical proof of the answer. Clearly we aren't any smarter than the public figures who couldn't comprehend this puzzle a half a century ago-- so it all in the framing of the problem?

sukilot 12y ago
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

sukilot 12y ago

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