The term probability refers to ‘an event’ the happing and non-happening of which is uncertain, or contingent. Literally, it means a chance, a possibility, likelihood, or an odd. In usage, it is expressed in a statement as follows:
(i) Possibly it will rain today.
(ii) There is a chance of your getting a first class.
(iii)This year’s profit likely to exceed the profits of all the preceding years.
(iv)The odds are 6: 5 in favour of his success.
Mathematically it is a number which is expressed either in the form of a faction, a percentage, or a decimal. When the happening of the event is predicted to be certain, the value of the probability is taken to be unity, i.e. 1, and when it’s happening is predicted to be impossible, the value of the probability is taken as 0 (zero). Thus, the value of a probability ranges from 0 to 1 and it is never negative.
Hence, the term probability may be defined “as a quantitative value of a chance that an event will take place in the face of favourable and unfavourable ways both of which are equally likely”.
P (E) = m/m+n
Where, p (E) = the probability of happening of an even E.
m = the number of favourable ways in which an event E can take place.
And n = the number of unfavourable ways in which an even cannot take place.
Further, the probability of not happening of an even can be represented thus:
q (E) = m/m+n
Where, q (E) represents probability of not happening of an event E.
It must be noted that sum of the probability of happening and that of not-happening would amount to unity, i.e., 1, thus symbolically p+q =1.