:I think people do understand the difference, but its slippery and they don't think about it much of the time.  If you presented it like this:  When the host opens a door at random he reveals a goat 2/3 of the time and the car 1/3 of the time but when chooses to open a door he knows hides a goat he reveals a goat 3/3 of the time. I think few people would disagree or even have any qualms about accepting it.  That still doesn't mean that every time they think of the host opening door at random to reveal a goat they are going to realize that 'opening the door at random' is the meaningful part and revealing the goat is merely incidental.