Did any of those readers of her column, including PhD and mathematicians, that declared her solution wrong do so because they objected to the clarification? (Does it make sense to declare the answer wrong ignoring the answer?)
I think they didn't notice the significance of that clarification (which, again, was given in the context of a modified problem). Reading the exchanges again, though, I see that many respondents were not only mistaken, but also impolite or sexist in accusing Marylin of being wrong.
If you specify the problem carefully, anyone with some training in probability should get the answer right. But clearly back then it was a head scratcher.
I wonder whether there've been other problems like that, or we will encounter similar ones: elementary and easy to understand, yet many people get it confidently wrong, until the correct solution permeates through culture.
The original problem is the one you're thinking of as modified, since the original problem was about a real-world game show, and the rules of the real-world show in question included Monty Hall (the host) opening a door that the player hadn't picked and which did not contain the car. The problem assumed familiarity with the game show, the clarification is for people who didn't watch the show.
> [that clarification] was given in the context of a modified problem
I don’t understand what do you mean by that. The clarification was part of the original answer in the context of the original question. The clarification was stated again and again and again. If that’s a “modified problem” so be it but that was the problem being discussed with her readers.
Ok, so the modification was the "Here’s a good way to visualize what happened." explanation.
I would say that the whole (short) paragraph is intended to clarify why the answer to the question is "Yes; you should switch."
Maybe it was not a good way to visualize what happened after all. Experience shows that some readers were unable to understand the argument.
However, none of them complained about the explanation being wrong because those were two completely different problems (only in the second one the host will always avoid the door with the prize, apparently).
