Basic Concepts used in Probability Theory

The following definitions and terms are used in studying the theory of probability.

Random experiment: 

Random experiment is one whose results depend on chance, that is the result cannot be predicted. Tossing of an unbiased coins, throwing of  fair dice are some examples of random experiments.

Trial:

Performing a random experiment is called a trial.

 Outcomes: 

The results of a random experiment are called its outcomes. When two coins are tossed the possible outcomes are HH, HT, TH, TT.

Event:

An outcome or a combination of outcomes of a random experiment is called an event.

For example tossing of a coin is a random experiment and getting a head or tail is an event.

Sample Space:

 Each conceivable outcome of an experiment is called a sample point. The totality of all sample points is called a sample space and is denoted by S. For example, when a coin is tossed, the sample space is S = { H, T }. H and T are the sample points of the sample space S.

Equally likely events:

Two or more events are said to be equally likely if each one of them has an equal chance of occurring. For example in tossing of a coin, the event of getting a head and the event of getting a tail are equally likely events.

Mutually exclusive events:

Two or more events are said to be mutually exclusive, when the occurrence of any one event excludes the occurrence of the other event. Mutually exclusive events cannot occur simultaneously.

For example when a coin is tossed, either the head or the tail will come up. Therefore the occurrence of the head completely excludes the occurrence of the tail. Thus getting head or tail in tossing of a coin is a mutually exclusive event.

Exhaustive events:

Events are said to be exhaustive when their totality includes all the possible outcomes of a random experiment. For example, while throwing a die, the possible outcomes are

{1, 2, 3, 4, 5, 6} and hence the number of cases is 6.

Complementary events:

The event ‘ A occurs’ and the event ‘ A does not occur’ are called complementary events to each other. The event ‘A does not occur’ is denoted by A′ or A or Ac. The event and its complements are mutually exclusive. For example in throwing a die, the event of getting odd numbers is { 1, 3, 5 } and getting even numbers is {2, 4, 6}.These two events are mutually exclusive and complement to each other.

Independent events:

Events are said to be independent if the occurrence of one does not affect the others. In the experiment of tossing a fair coin, the occurrence of the event ‘ head’ in the first toss is independent of the occurrence of the event ‘ head’ in the second toss, third toss and subsequent tosses.

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