Suppose in a large number of trials the sample space S contains N sample points. The event A is defined by a description which is satisfied by NA of the occurrences. The frequency interpretation of the probability P(A) of the event A, tells us that P(A) = NA/ N.
A purely mathematical definition of probability cannot give us the actual value of P(A) and this must be considered as a function defined on all events. With this in view, a mathematical definition of probability is enunciated as follows:
“Given a sample description space, probability is a function which assigns a non – negative real number to every event A, denoted by P(A) and is called the probability of the event A.”