There is a huge urn full of marbles, each marked with a single digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. The marked marble quantities are uniformly distributed between all of the digits and the marbles are thoroughly mixed. You look away, choose 10 marbles, and put them in a black velvet bag.
When you have some time, you look away, open the bag, and remove one marble. You close the bag, look at the digit on the marble, open a beer perhaps, and calculate the probability that there is at least one more marble in the bag with the same digit.
The answer is brute forced below is there a formal way to obtain the answer? I don't believe the marbles-in-urn standby, the hypergeometric distribution, is any help at all.
Copy and paste the algorithm below into Mathematica (V6 or newer) to find the surprising answer, estimated from a million tests in about 16 seconds.