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Such that the contestant chooses 1 door, the host then opens 98, and they are given the opportunity to switch to the last remaining door? That's actually a pre
by Crito 13y ago
Such that the contestant chooses 1 door, the host then opens 98, and they are given the opportunity to switch to the last remaining door?
That's actually a pretty brilliant way of explaining it. With numbers like that the answer becomes much more intuitive.
- logicallee 13y agoWhy 100? Why not just 5? Some people would 'get' it at five, some people at 100, and some people at a million. If you have to choose out of a million doors, and no matter what the host opens all but one of them, so that your prize is either behind the door you picked, or behind the other one -- then should you switch your choice? Well, obviously, you should - with a million doors, it becomes obvious that you have just a 1 in 1,000,000 chance of having picked it. But thing is - that "obvious" thing 'should' be just as obvious with 1000 doors, 100, 20, 5, or...3.... It's a matter of degree - not kind. So appealing to a way of intuiting it that is a lot more 'obvious' - while in fact having the exact same format of question, just goes to underscore how fickle intuition can be. That said, taking individual variables to ridiculous extremes is a great way to thought experiment and an awesome way to get intuition to work better.
- Crito 13y agoYeah, I'm not wed to a particular number... I'm just observing that larger numbers seem to make it more intuitive than, say, 3 doors.