RANDOM EXPERIMENT IN PROBABILITY

An experiment may be described as a performance that produces certain results.

An experiment is defined to be random if the results of the experiment depend on chance only.

For example if a coin is tossed, then we get two outcomes—Head (H) and Tail (T).

It is impossible to say in advance whether a Head or a Tail would turn up when we toss the coin once. Thus, tossing a coin is an example of a random experiment.

Similarly, rolling a dice (or any number of dice), drawing items from a box containing both defective and non—defective items, drawing cards from a pack of well shuffled fifty—two cards etc. are all random experiments.

Tossing a coin is a good example of random experiment.  Because, we can not predict in advance whether it will turn up head or tail.

In order to develop a sound knowledge about probability, it is necessary to get ourselves familiar with a few terms.

Let us look at the important terms which are related to the stuff probability.

Events

The results or outcomes of a random experiment are known as events. Sometimes events may be combination of outcomes.

The events are of two types :

(i) Simple or Elementary,

(ii) Composite or Compound.

An event is known to be simple if it cannot be decomposed into further events.

Tossing a coin once provides us two simple events namely Head and Tail. On the other hand, a composite event is one that can be decomposed into two or more events.

Getting a head when a coin is tossed twice is an example of composite event as it can be split into the events HT and TH which are both elementary events.

Mutually Exclusive Events or Incompatible Events

A set of events A1, A2, A3, …… is known to be mutually exclusive if not more than one of them can occur simultaneously.

Thus occurrence of one such event implies the non-occurrence of the other events of the set.

Once a coin is tossed, we get two mutually exclusive events Head and Tail.

Exhaustive Events

The events A₁, A₂, A₃, ………… are known to form an exhaustive set if one of these events must necessarily occur.

As an example, the two events Head and Tail, when a coin is tossed once, are exhaustive as no other event except these two can occur.

In other words, if two or more events together comprise the sample space, then those events are called as exhaustive events.

Equally Likely Events or Mutually Symmetric Events or Equi-Probable Events

The events of a random experiment are known to be equally likely when all necessary evidence are taken into account, no event is expected to occur more frequently as compared to the other events of the set of events.

The two events Head and Tail when a coin is tossed is an example of a pair of equally likely events because there is no reason to assume that Head (or Tail) would occur more frequently as compared to Tail (or Head).

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