Probabilities:

If x_i is a possible outcome of X, we define a probability:

P(X=x_i)

which is abbreviated to P(x_i) when there is no possibility of confusion about which event is meant. Similar notation uses |X=x_i| for the number of times x_i occurs during a collection of trials. The probability of an outcome is defined to be the limit of the ratio between the number of times the outcome occurs and the number of trials attempted. Our sketchy formal definition of probability is:

This sort of model is applicable to many situations in data-intensive linguistics including some situations which we describe in more detail later in this chapter.