re: Marilyn vos Savant and the history of the Montel Hall question

This actually a fairly smart question for fairly smart people.

The answer is counterintuitive - but it is correct from a probability standpoint.

However, it is the nature of the 1/3 and of the laws of probability itself.

The original choice is a 1 in 3. The fact that it eliminates one of the 2 bad choices inherently increases your odds - you cannot switch from a bad answer to a bad answer but only from bad to good or good to bad.

All of the failures occur on the initial choice (picking the right one) - all of the successes occur on the switches (switching from the bad one, with the other bad one eliminated).

Weird, but it works.

(Because they never show you the good choice if you pick one of the bad - that's the other factor that makes this work.)