This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with in-service teachers. In both, the participants pretended to be secondary school students. In a third activity, students use a calculator program to determine the theoretical probability. A common misconception about random samples is that outcomes are "spread out" more or less evenly among possible results. However, students need to develop an understanding that sometimes results within a given random sample are clustered or repeated. Students must also understand that the distribution within a particular sample is not always uniformly or symmetrically distributed among the possible results. Performing simulations like the ones described here can help students develop such understanding. (Contains 2 tables and 4 figures.)