[jibal]

"Once you develop intuition, probability is really quite intuitive"

That's a tautology.

Plenty of studies, such as the work by Kahneman and Tversky, show that humans by default have incorrect statistical intuitions. These faulty intuitions are hard to overcome, even by a considerable amount of training.

> The Monte Hall problem is more of a curiosity than a fundamental principle!

It's quite straightforward conditional probability. That so many people, including trained mathematicians, get it wrong is quite illustrative. And it's not unique ... the coins and drawers problem is similar, and one can craft many others. MH is not a mere curiosity, it's simply well known.

[jonsen]

> It's quite straightforward ...

No it is not, unless it is explicitly stated that Monty knows where the car is and that he deliberately opens a door with a goat. Just look at the discussions in the comment here.

[542354234235]

> unless it is explicitly stated that Monty knows where the car is and that he deliberately opens a door with a goat.

That has been part of the explicit problem ever since it was first presented back in 1975.

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?"

[jonsen]

It does not clearly say that it is Monty’s procedure to

- allways open a door

- allways open a door with a goat

- and not open a door at random

Often discussion of the solution reveals that this is not clear.

[542354234235]

There are three doors. You have picked one, leaving two other doors. It absolutely explicitly says he opens one door. The only options are a goat or a car. If it was a car, you would have lost already and so there is no problem. If it was random, you still get the same information (what is behind one of the unpicked doors).

[jonsen]

> If it was random, you still get the same information

No, if both you and Monty pick a door at random, there’s 1/3 chance of a car behind each door. If Monty’s door reveals a goat, it’s 50/50 for the remaining two doors. It’s mandatory to specify Monty’s procedure precisely.

[jibal]

This is goalpost moving that has nothing to do with the original point. If people misunderstand the conditions of the problem, that has nothing to do with intuitions about probability.

I won't respond further.

[jonsen]

> nothing to do with the original point.

Agree, but my point is that the Monty puzzle is a bad example to use educational if not careful.

[mturmon]

It is a tautology, but we are studying teaching, so maybe that's not unexpected? ;-)

My point is that the goal of the course should be to understand principles, not to teach people that their existing intuition is faulty. Who cares about their prior condition of ignorance?

For more, see my reply nearby.