Probability of a "hit" when revealing 10 cards.

Question

The premise is: I have 10 cards to flip over. 5 are from set A and 5 from set B. One of these 10 cards has a special marking on it. My question is, what is the appropriate order to flip cards from set A and B to maximize the chances that the "special" card is from set B? Here's an example:

For instance, I know the probability of flipping the special card on the first flip is 1/10. This could either be from set A or B (50% chance either way). I'd rather flip a card from set A, right? Because the odds are so low that it is actually the special card. Now let's assume we flip A and find it is not the special card. On the second flip, there is a 4/9 chance for the special card to be from set A and 5/9 chance for set B. The odds are improving for set B. Is there a most "optimistic" order to flip these cards to maximize the special card being from set B?

Answer 1

No matter what order you flip in, the card has a probability of 1/2 of being in set B. Now, if you want to know what order to flip in which maximizes the probability on a particular flip that the card is in set B, then make your first five flips in A. If the card is indeed in B, then before flip 6, and possibly flips 7, 8, 9, and 10, the probability is 100% that the card is in B.