When we speak about the probability of observing events such as the outcome of a toss of a coin, we are implicitly assuming some kind of model, even in this simple case. In the case of a coin, the model would state that there is some certain, fixed probability for the particular outcomes. This model would have one parameter, p the probability of the coin landing on heads. If the coin is fair, then p=0.5. We can then speak about the probability of observing an event, given specific parameter values for the model. In this simple case, if p =0.5, then the probability of the coin landing heads on any one toss is also 0.5.

In the case of this simple example, it does not seem that we have gained very much - we seem to be merely calling what was previously a simple probability the parameter of a model. As we shall see, however, this way of thinking provides a very useful framework for expressing more complex problems.