Experiment

The word experiment means an operation, which can produce well defined outcomes. The are two types of experiment:

(i) Deterministic experiment (ii) Probabilistic or Random experiment

DETERMINISTIC EXPERIMENT:

Those experiments which when repeated under identical condition produced the same results or outcome are known as deterministic experiment. For example, Physics or Chemistry experiments performed under identical conditions.

PROBABILISTIC OR RANDOM EXPERIMENT:

In an experiment, when repeated under identical conditions donot produce the same outcomes every time. For example, in tossing a coin, one is not sure that if a head or tail will be obtained. So it is a random experiment.

SAMPLE SPACE:

The set of all possible outcomes of a random experiment is called a sample space associated with it and is generally denoted by S.

Ex. When a dice is tossed then S = {1, 2, 3, 4, 5, 6}.

EVENT:

A subset of sample space associated with a random experiment is called an event. For example, in tossing a dice getting an even number is an event.

FAVOURABLE EVENT:

Let S be a sample space associated with a random experiment and A be event associated with the random experiment. The elementary events belonging to A are known as favourable events to the event A. For example, in throwing a pair of dice, A is defined by "Getting 8 as the sum". Then following elementary events are as outcomes: (2, 6); (3, 5); (4, 4); (5, 3); (6, 2). So, there are 5 elementary events favourable to event A.

COMPLEMENTARY EVENT:

Let E be an event and (not E) be an event which occurs only when E does not occur.

The event (not E) is called the complementary event of E.

Clearly, P(E) + P(not E) = 1.

∴ P(E) = 1 – P(not E).