Probability Question

[panthers63]

Probability hasn't changed at all. If you cant go with your choice I'd advise using the exit door.

[wagon596]

Yes, same theory was in the movie "21" so I'm not going to tell. Goodluck people.

[Tiarra]

Ah, and the solution!

Well, think of it this way. When the dealer has the 3 cards laid out on the table, you have a 1:3 chance of picking the Ace. However, after you pick your card and BEFORE it is revealed, we can separate our cards into 2 stacks -- stack ONE with your 1 card in it and stack TWO with the 2 cards you didn't pick. Obviously, stack ONE has a 1:3 chance of having the ACE and stack TWO has a 2:3 chance of having the ACE, since they have one and two cards respectively. But the dealer knows what the cards are, and he always turns over one of the cards from stack TWO and it is always a deuce.

Before the dealer does this, we have stack ONE with card A with a 1:3 chance, and stack TWO with cards B&C with a 2:3 chance.

Stack ONE: Card A 1:3
Stack TWO: Card B 1:3
Card C 1:3

after the dealer reveals one of the cards from stack TWO to be a deuce (for example, he flips over card C to reveal a deuce) there is still a 1:3 chance that the Ace was in Stack ONE and a 2:3 chance it was in stack TWO. THAT HAS NOT CHANGED. What has changed is we now know that card C is not the Ace, and therefore card B has a 2:3 chance of being the Ace while card A stays with its 1:3 odds.

Stack ONE: Card A 1:3
Stack TWO: Card B 2:3
Card C 0:3

For an explanation by Ms. Vos Savant herself, click the following link.....

Marilyn vos Savant | The Game Show Problem