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

where is the number of times the outcome occur in the sample, is the total number of points in the sample, and the over the is to denote that it is an estimate of the true (unknown) probability .

**Example:**- Consider flipping a thumbtack (a flat-headed drawing pin, like you would put on someone's chair during your school days). It can land with the point pointing up or with the point touching the ground. What is the probability that it lands pointy side up? To answer this, we can do some experiments. Suppose we flip a thumbtack 20 times, and it comes up pointy side up 13 times and pointy side down times. Our estimate of the probability of a thumbtack landing with pointy side up would be .

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 .