> and the host, who knows what’s behind the doors, opens another door ... which has a goat
The explanation Marylin originally wrote makes the second assumption explicitly clear to avoid any possibility of confusion
> Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
People still wrote in claiming she was wrong.
> Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful.
She then explained the solution a second time with a table clearly illustrating the assumptions and the odds.
People continued to write in claiming she was wrong.
> I’m receiving thousands of letters, nearly all insisting that I’m wrong
> 92% are against my answer, and and of the letters from universities, 65% are against my answer.
Lack of clarity did not generate all the letters.
I run a small website with logic puzzles. I get thousands of emails. Some tell me the problem is misleading. Some tell me the answer is wrong.
The one thing I have learned is that once someone's mind is made up, it will never change.
The other thing I have learned, is that a good problem is succinct.
The smartest people in the room will ask clarifying questions to test out their assumptions before they even attempt an answer.