A generalized version of the birthday problem is as follows. Suppose each member of a population independently receives a number of randomly selected from {1,2,3, ... , x}, and a random sample of size n is to be taken. If 0 < p < 1, what is the smallest value of n so that the probability that at least two of the sample have the same number is at least p? Both empirical modeling and approximation techniques are used to determine n as a function of x when p is fixed. An error analysis of the approximation is presented.
