# Random Experiments and Events, Objectives, Random Experiment

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• In day-to-day life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting either a ‘Head’ or a “Tail’ are two possible outcomes. (Assuming that the coin does not stand on the edge).

• If we throw a die (of course fair die) the possible outcomes of this activity could be any one of its faces having numerals, namely and at the top face.

• An activity that yields a result or an outcome is called an experiment. Normally there are variety of outcomes of an experiment and it is a matter of chance as to which one of these occurs when an experiment is performed.

• In this lesson, we propose to study various experiments and their outcomes.

## Objectives

After studying this lesson, you will be able to:

## Random Experiment

Let us consider the following activities:

(i) Toss a coin and note the outcomes. There are two possible outcomes, either a head (H) or a tail (T).

(ii) In throwing a fair die, there are six possible outcomes, that is, any one of the six faces 1, 2, 6.... may come on top.

(iii) Toss two coins simultaneously and note down the possible outcomes. There are four possible outcomes, HH, HT, TH, and TT.

(iv) Throw two dice and there are 36 possible outcomes which are represented as below:

I.e. outcomes are

----- ----- -----

----- ----- ------

Each of the above mentioned activities fulfil the following two conditions.

(a) The activity can be repeated number of times under identical conditions.

(b) Outcome of an activity is not predictable beforehand, since the chance play a role and each outcome has the same chance of being selection. Thus, due to the chance playing a role, an activity is

(i) Repeated under identical conditions, and

(ii) Whose outcome is not predictable beforehand is called a random experiment.

Example:

Selecting a chair from chairs without preference is a random experiment. Justify.

Solution:

(a) The experiment can be repeated under identical conditions.

(b) As the selection of the chair is without preference, every chair has equal chances of selection.

Hence, the outcome is not predictable beforehand. Thus, it is a random experiment.

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