Terms Related to Probability

Computation of correct value of probability depends greatly upon a clear understanding of certain terms connected with the theory of probability. Some of them are explained here as under:

(a)  Experiment. It is an operation which produces some result or outcome. Tossing a coin, rolling a die, drawing a card from a pack of playing cards, drawing a ball from a bag of different balls, observing the defective items produced by a machine, and recording the number of customers visiting a shop are the examples of an experiment.

(b)  Space. It is a set of all possible results, or outcomes of an experiment. It is represented symbolically by S = {             }. Thus, if two coins are tossed, the various possible outcomes are two heads – HH, two tails – TT, first one head and second one tail – HT, first one tail and second one head – TH. The set of all these possible outcomes constitutes a sample space which is represented as thus,

S = {HH, TT, HT, TH}.

It is to be noted that a sample space is also known as an exhaustive set of the events.

(c)  Sample Point. Each one of the possible results of an experiment represented as an element of a sample space is called a sample point. Thus, in the example given above, HH, TT, HT, and TH are the different sample points belonging to the sample space – S.

(d)  Event. An event is a case of interest which has the capability of happening, or taking place to a market extant. It is a subset of a sample space for an experiment which is represented by some alphabet. Thus, in the above example, if the case of an interest is ‘both coins fall alike’, the event will be represented as follows :

E = {HH, TT, alike}.