In earlier classes, we studied about the concept of probability as a measure of uncertainty of various phenomenon. We have obtained the probability of getting an even number in throwing a die as 3/6 or 1/2. Here the total possible outcomes are 1,2,3,4,5 and 6 (six in number).
The outcomes in favour of the event of ‘getting an even number’ are 2,4,6 (i.e., three in number). In general, to obtain the probability of an event, we find the ratio of the number of outcomes favourable to the event, to the total number of equally likely outcomes. This theory of probability is known as classical theory of probability.
The probability on the basis of observations and collected data, is called statistical approach of probability. Both the theories have some serious difficulties. For instance, these theories can not be applied to the activities or experiments which have infinite number of outcomes. In classical theory we assume all the outcomes to be equally likely. The outcomes are called equally likely when we have no reason to believe that one is more likely to occur than the other. In other words, we assume that all outcomes have equal chance (probability) to occur.
Thus, to define probability, we used equally likely or equally probable outcomes. This is logically not a correct definition. Thus, another theory of probability was developed by A.N. Kolmogorov, a Russian mathematician, in 1933. He laid down some axioms to interpret probability, in his book ‘Foundation of Probability’ published in 1933.
Sample space: The set of all possible outcomes
Sample points: Elements of sample space
Event: A subset of the sample space
Impossible event: The empty set
Sure event: The whole sample space
Complementary event or ‘not event’: The set A′ or S - A
Event A or B: The set A ∪ B
Event A and B: The set A ∩ B
Event A and not B: The set A - B
Mutually exclusive event: A and B are mutually exclusive if A ∩ B = φ
If A and B are mutually exclusive, then P(A or B) = P(A) + P(B)
Equally likely outcomes: All outcomes with equal probability