If the probability of an event can be calculated even before the actual happening of the event, that is, even before conducting the experiment, it is called Mathematical probability. If the random experiments results in ‘n’ exhaustive, mutually exclusive and equally likely cases, out of which ‘m’ are favourable to the occurrence of an event A, then the ratio m/n is called the probability of occurrence of event A, denoted by P(A), is given by
P (A) = m/n = Number of cases favourable to the event A/Total number of exhaustive cases
Mathematical probability is often called classical probability or a priori probability
because if we keep using the examples of tossing of fair coin, dice etc., we can state the
answer in advance (prior), without tossing of coins or without rolling the dice etc.,
The above definition of probability is widely used, but it cannot be applied under the
(1) If it is not possible to enumerate all the possible outcomes for an experiment.
(2) If the sample points (outcomes) are not mutually independent.
(3) If the total number of outcomes is infinite.
(4) If each and every outcome is not equally likely.