Quote:
Originally posted by Sidd Finch
I've read this before and disagree with it. And decided that Marilyn vos Savant is a skanky whore.
As I read the explanation, the odds don't change if there is no interference -- i.e., if you pick one of three doors, and I eliminate a wrong door, the odds of you getting the right door by switching are 50/50.
The statistics change if Monty Hall is telling you to switch. And I think that this is not a matter of probability, but a matter of statistics -- the two are different and the difference is important; probability is math, statistics is history.
The problem immediately gets into an area where statistics becomes useless -- Monty knows where the car is. What if he doesn't like you? Is constipated and cranky that day? Had a booze-and-hooker filled night and makes a mistake?
Anyway, that's my 2 cents.
|
Think of it this way:
I place 52 playing cards face down and ask you to pick which one is the ace of spades. You choose. I then flip over 50 other "non-ace of spade" cards (leaving the one you've chosen and one other card face down) and ask if you'd like to keep your first choice or switch to the one face down card.
When you chose your card, you had a 1/52 chance of picking the ace of spades. This does not change now that I've flipped 50 other cards over because that choice was made before I flipped the cards. Conversely, the chances that the ace of spades is one of the other cards is 51/52. Once I flip the other 50 cards, the chances that that single card I have left is the ace of spades is 51/52.
Your chances of having chosen the ace of spades from the deck of 52 have not shrunk from 1/52 to 1/2. Thus, you should switch cards because the chances the other card is the ace of spades is 51/52.
Now do the above example with 26 cards. 10 cards. 5 cards. Although the odds don't improve as drastically by switching, it's always better odds if you do switch. Even when you get down to three cards, you should still switch.
Using the Monty Hall example, your odds of picking the car are initially 1 in 3. The odds are 2/3 that one of the other doors has the car behind it. The odds remain 2/3 even once the goat is revealed. Thus, by switching doors your odds of winning the car increase from 1/3 to 2/3.
