[UATrewqaz]

My statistics professor explained this to me perfectly.

3 doors (1 car, 2 goats).

Thus you have a 1 in 3 chance (33%) of picking the right door.



A door is then revealed to you showing you 1 of the goats. So there are two doors remaining.

YOU SHOULD ALWAYS SWITCH (assuming they will always show you a goat, because they always can).

If you do not switch you have your 33% chance of picking correctly.

If you switch:
33.3% of the time you have the car and switch to the goat.
66.6% of the time you have a goat and are switching to the car.

Thus you have a 66% chance of winning the car if you switch.


Some people had a hard time understanding this so he had a great example.

He pulled out a deck of cards and said, you have to select the ace of spades, and a student selected 1 card (face down). He then took the remaining deck and began showing him cards, saying "Ok 4 of clubs" discarded it, etc etc etc

Until there was 1 only card left in his "deck"

So now there are two cards, the one the student picked and the one he has left (he has shown him 50 cards from the 51 remaining that aer NOT the ace of spades).

He then asked the student, "Do you wanna switch"
and of course the studen twas like "hell ya"

The odds of him having the ace of spades were nto 50% even though only 2 cards remained.