Unrepeatable experiments

In most scientific contexts, it is possible to imagine repeating an experiment in essentially the same way. However there are other scenarios in which such repetitions are clearly impossible, but there is still uncertainty about the outcome. For example,

There are no equally likely outcomes and the "experiment" cannot be repeated. Instead, a subjective or personal assessment of probability must be made.

Subjective probability

Subjective probability can be given a formal definition, based on what you would regard as a 'fair bet' for the event. If either of the earlier definitions of its probability can be used, this results in the same numerical value, provided it is applied by a 'reasonable' person with full knowledge of the experiment's structure.

Bayesian statistics

A whole field of statistics called Bayesian statistics is based on subjective probabilities and is gaining in importance

However we will neither deal with subjective probability nor Bayesian statistics further in this e-book.