Probability of error

In statistics, the term "error" arises in two ways. Firstly, it arises in the context of decision making, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. Secondly, it arises in the context of statistical modelling (for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring.
Hypothesis testing.
In hypothesis testing in statistics, two types of "error" are distinguished.
The probability of error is similarly distinguished. 
Statistical and econometric modelling.
The fitting of many models in statistics and econometrics usually seeks to minimise the difference between observed and predicted or theoretical values. This difference is known as an "error", though when observed it would be better described as a "residual". 
The error is taken to be a random variable and as such has a probability distribution. Thus distribution can be used to calculate the probabilities of errors with values within any given range.