The events B1,B2,...,B11 in Example 2.1.12 can be thought of in much the same way as the two eventsB1andB2 that determine the mixture of long and short bolts in Example 2.1.11. There is only one box of bolts, but there is uncertainty about its composition. Similarly in Example 2.1.12, there is only one group of patients,but we believe that it has one of 11 possible compositions determined by the events B1,B2,...,B11. To call these events, they must be subsets of the sample space for the experiment in question. That will be the case in Example 2.1.12 if we imagine that the experiment consists not only of observing the numbers of successes and failures among the patients but also of potentially observing enough additional patients to be able to computep, possibly at some time very far in the future. Similarly, in Example 2.1.11, the two eventsB1andB2 are subsets of the sample space if we imagine that the experiment consists not only of observing one sample bolt but also of potentially observing the entire composition of the box.

Throughout the remainder of this text, we shall implicitly assume that experiments are augmented to include outcomes that determine the values of quantities such asp. We shall not require that we ever get to observe the complete outcome of the experiment so as to tell us precisely whatpis, but merely that there is an experiment that includes all of the events of interest to us, including those that determine quantities like p.