Estimating of probability of discrete states is easiest. Given the
interpretation of probability discussed in
section , it is reasonable to use
the frequency of the outcome in the sample. In other words, the
estimate of the probability of the outcome is
It is important to emphasise that this is only an estimate of the true probability. Since there will always be fluctuations and variations in a finite sample, it is possible that the true probability is different from this estimate. For example, if the true probability was it would be possible to get this data, although this data would be less likely than data in which the frequency is closer to . Our estimate is the best estimate from the data in the sense that the data would be less likely if the probability was different. Thus, in a sense, this estimate is the mostly likely value given the data. For this reason, it is called a maximum likelihood estimate. This can be made more precise, see section .