What a shame that the title doesn't reveal what this is -- it's the original appearance of the Monty Hall problem, when Marilyn Vos Savant answered the problem correctly, only to be criticized (wrongly) by any number of well-educate academics, like this one:
"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. -- Robert Sachs, Ph.D."
Doctor Sachs was entirely wrong, as were about ten thousand other academics who ganged up on Vos Savant in the months following the appearance of this column.
The real outcome is that, if the contestant doesn't change doors, his probability of winning is 1/3, but if he does change doors, his chance goes up to 2/3. Details:
http://en.wikipedia.org/wiki/Monty_Hall_problem
"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. -- Robert Sachs, Ph.D."
Doctor Sachs was entirely wrong, as were about ten thousand other academics who ganged up on Vos Savant in the months following the appearance of this column.
The real outcome is that, if the contestant doesn't change doors, his probability of winning is 1/3, but if he does change doors, his chance goes up to 2/3. Details:
http://en.wikipedia.org/wiki/Monty_Hall_problem