> But we do know: it's always on purpose, Monty never opened a door with a car behind it We only know that if the problem tells us. Sometimes it doesn't. > Th

> But we do know: it's always on purpose, Monty never opened a door with a car behind it We only know that if the problem tells us. Sometimes it doesn't. > There are no ambiguities in the Monty Hall problem The problem has been written up thousands of times. I'm sure that some writeups are sufficiently unambiguous, but many are not. For example, consider the two "variants" described by this comment https://news.ycombinator.com/item?id=8664550 https://news.ycombinator.com/item?id=8664550 > The host selects one of the doors with a goat from the remaining two doors, and opens it. > The host chooses one of the remaining two doors at random and opens it, showing a goat. This commenter was trying hard for semantic precision, and yet, I think if you encountered the first variant in isolation it would be perfectly reasonable to interpret it as "The host [randomly] selects one of the doors with a goat [although he might have selected the prize]" even though this is clearly not what the commenter was attempting. If you disagree, that only proves my point: this problem is prone to silly and wasteful semantic debate, rather than the interesting probability result it should be focused on.