Comment by kergonath

> it could be that the host always shows a goat

That’s what the sentence says: “and the host, who knows what's behind the doors, opens another door […] which has a goat”.

> or the host shows something at random and we just look at the cases where he shows a goat

Nothing says that the host opens a door at random. Quite the contrary, we know that the host has a perfect knowledge of the situation.