The simple mathematical model for this is a Poisson distribution. If you search the Internet you can easily find information about it, and you can probably find code samples for calculating the probabilities.
The Poisson distribution assumes that events are completely random. In real life this is rare. For example, a user of your application might tend to perform more than one action in the space of a few minutes. This causes some clustering of the events, making the Poisson distribution less accurate. But still it should provide estimates that have some meaning.