Math odds question: picking cards
May 31st, 2011 at 1:23:01 PM
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Hi, I'm a long time lurker, first time poster. I was hoping that you local experts could help out with a probability question that I had.
Suppose you shuffled N cards numbered 1 through N. You pick 1 card at a time, if you pick the card numbered 1, you keep the card and try for the 2-card; otherwise the card is turned back over and you continue to look for the same number. This continues, trying to find each card in turn. The cards are never reshuffled, so that once you've found a card out of order, you should know where it is for later when you are looking for that number. Is there a formula to compute the probability of picking X correct cards within P picks. (That is, if you start with 10 cards, what are the odds that you will find 10 cards (9 cards? ...8 cards?) in order after 10 picks?)
I have found a few rules to computer specific cases, but nothing to compute a general case. I'm sure with the cumulative mind power here that someone will be able to help.
Suppose you shuffled N cards numbered 1 through N. You pick 1 card at a time, if you pick the card numbered 1, you keep the card and try for the 2-card; otherwise the card is turned back over and you continue to look for the same number. This continues, trying to find each card in turn. The cards are never reshuffled, so that once you've found a card out of order, you should know where it is for later when you are looking for that number. Is there a formula to compute the probability of picking X correct cards within P picks. (That is, if you start with 10 cards, what are the odds that you will find 10 cards (9 cards? ...8 cards?) in order after 10 picks?)
I have found a few rules to computer specific cases, but nothing to compute a general case. I'm sure with the cumulative mind power here that someone will be able to help.
