The data considered are the outcomes of independent binomial events and the number of events resulting in success is of interest. The assumption or trials from a binomial population is often made, even when evidently unjustifiable. This paper shows that this assumption is often unnecessary and also can lead to difficulties in deciding on other assumptions. These difficulties and the use of a more general probability model are illustrated by a study of surgical mortality probability. It is found that the situation of unequal event probabilities can often be approximated by considering that the events are trials from a binomial population with success probability equal to the arithmetic average of the event probabilities. With this interpretation, results based on the assumption of a binomial population remain applicable.