We had learnt about the experimental (or empirical) probabilities of events which were based on the results of actual experiments.
Probabilities are based on the results of an actual experiment. Experimental probabilities are based on the results of actual experiments and adequate recordings of the happening of the events. Moreover, these probabilities are only ‘estimates’.
Suppose a coin is tossed at random.
We can reasonably assume that each outcome, head or tail, is as likely to occur as the other. We refer to this by saying that the outcomes head and tail, are equally likely.
Assume that all the experiments have equally likely outcomes.
P(E) = Number of trials in which the event happened/Total number of trials
The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as -:
P(E) = Number of outcomes favourable to E/Number of all possible outcomes of the experiment
In general, it is true that for an event E,
P( E ) = 1 — P(E)
The event E , representing ‘not E’, is called the complement of the event E. We also say that E and E are complementary events.