just the fact that we have SO many comments here (and always when it comes to this topic) about how this problem can be misunderstood (e.g. knowing that the showmaster will never open the winning door before yours and that he will ALWAYS show you a blank door), means that we don't quite know how bad people are in intuitively understanding the probabilites because the real problem here (and elsewhere) was the meaning of the question, not (only) finding the answer. Nonetheless, we have a lot of studies that show how bad we are with probabilites (e.g. that the probability of two defined rare things happening at the same time is not only rare but extremely rare - unless they are interconnected of course) so there is certainly truth in here, but not quite as much as it appears at first. Nonetheless, I really like how much more intuitively clear the problem gets once you're talking about 100 doors instead of 3: So if the question were: "You're taking 1 out of 100 doors, say number 27, and then the rules of the game say that the showmaster must open 98 of the other doors that all hold a goat, meaning only your door and another are remaining. In one of those is certainly the price. Will it be rather in yours or in the other? Remember that you chose randomly out of 100 doors while the shomaster had to take care not to take out the winning door when he took out the other 98 doors (unless it was already your number 27, then he could have chosen freely). So where is probably the price?"