Re^6: Marilyn Vos Savant's Monty Hall problem

Please read Re^4: Marilyn Vos Savant's Monty Hall problem carefully, especially where I wrote

the host knows and will not open the door with the car (emphasis mine)

The knowledge Mr. Hall has and how he uses it is unambiguous. He always opens a door, he never opens the door with the car. and he always offers a switch. What's more important than the information he has is the information he provides by using what he knows in a predictable way.

I fully understand your previous node, and actually we are in agreement about the necessary information to calculate the probablilities. We just differ on what the original problem statement is and/or what assumptions can be safely made for this specific problem.

Re the spooky math problem: what I wrote were my initial thoughts when I read that root node. I'll reserve judgement and not argue either side until I investigate further (depends on life, kids, the missus etc. if I ever get to it). From what I've seen, if you are this sure you are right then you probably are. I've seen stranger things with my own eyes, so I won't rule out any possibility.

Comment on Re^6: Marilyn Vos Savant's Monty Hall problem

Replies are listed 'Best First'.
Re^7: Marilyn Vos Savant's Monty Hall problem by tilly (Archbishop) on Aug 23, 2004 at 20:42 UTC
Please read Re^4: Marilyn Vos Savant's Monty Hall problem carefully, especially where I wrote the host knows and will not open the door with the car (emphasis mine) The knowledge Mr. Hall has and how he uses it is unambiguous. He always opens a door, he never opens the door with the car. and he always offers a switch. What's more important than the information he has is the information he provides by using what he knows in a predictable way. Your memory is fooling you. As is pointed out at Re^4: Marilyn Vos Savant's Monty Hall problem, the original statement of the problem when Marilyn Vos Savant gave it was, 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Note that how the host uses his information is ambiguous in that problem statement. Furthermore most of the time when this comes up for discussion, the problem is even less carefully stated than that. It is typically not even specified that the host knows where the car is. For example look at the node that started this discussion, Marilyn Vos Savant's Monty Hall problem. Therefore no matter how much you'd like to believe that you've never seen it poorly stated, you're wrong. In fact you've seen it poorly stated at least twice already today.	[reply]
Re^8: Marilyn Vos Savant's Monty Hall problem by bmann (Priest) on Aug 23, 2004 at 23:06 UTC
Your memory is fooling you... Hmmph. Good call - I was wrong about what I inferred about the puzzle and what was actually asked. However rational the assumptions I made were, the original question posed to Ask Marilyn was ambiguous about Monty's behavior.	[reply]