[jncfhnb]

Incorrect. You have no way to know if he would only show you a goat if you picked the car.

If that were the case then switching is a guaranteed loss. Simply knowing that he opened a door and showed a goat does not mean he would have done this regardless of your choice.

Not a probability problem without this info.

[bemusedthrow75]

> You have no way to know if he would only show you a goat if you picked the car.

What do you mean?

It's specified in the scenario. He shows you a goat. It's right there. This isn't a variable. It's a fact.

Your only job is to work out whether, given the scenario described, it makes sense to switch. Given all your possible choices.

[jncfhnb]

You cannot assume that your context would apply from all starting conditions!

That’s why this problem is kind of bad. It does not describe the behavior of the host. It describes the perspective of a contestant halfway through the game.

Dumb example. Host flips a coin 9 times in a row and lands heads each time. If you believe this to have happened by chance then it’s probably rigged because that’s insane and it’ll likely be heads again.

If it’s ALWAYS heads then you haven’t learned anything.