Stan Brown wrote: > > Problem posed me by a student: ten persons (A through J) and ten > envelopes containing cards marked with letters A through J. (Each > letter is in one and only one envelope.) > > The random variable x is the number of people who get the "right" > envelope when the envelopes are handed out randomly. Obviously > 0 <= x <= 10. > > Question: How do we express the probability distribution P(x)? > > I've done some work on this, and I _must_ be missing something > obvious. Here's part what I've got so far. > > 10! = number of possible arrangements. Only one of them assigns all > ten envelopes to the right people, so > P(10) = 1/10! > > If nine people get the right envelopes, the tenth must also get the > right envelope. So > P(9) = 0 > > I bogged down on figuring P(8), though. Then I tried to look at P(0) > and got even more bogged down. > > Am I missing something here? Is there an elegant way to write > expressions for the probabilities of the various x's?
This is sometimes called the matching problem or the matching experiment. Type "letters envelopes random" into google and you get several relevant hits - e.g. http://www.math.uah.edu/stat/urn/urn6.html http://www.wku.edu/~neal/probability/matching.html either of these might be enough for you to see how to do it. If you put "matching" in there as well it would probably target your search better, but I just wanted to show you you didn't need more than your own description of the problem to find out lots just with google. Glen ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
