Page 11 - DMTH404_STATISTICS

Unit 1: Sample Space of A Random Experiment

Experiment 8 : A group of ten persons is classified according to their blood groups 0, A, B and AB. Notes
The number of persons in each group may vary between 0 and 10, subject to the frequencies of
all four classes adding up to 10.
Experiment 9 : The number of accidents along the Bombay-Bangalore national highway during
the month is noted.

Experiment 10 : A radio-active substance emits particles called a-particles. The number of such
particles reaching an observation screen during one hour is noted.
Experiment 11 : Thirteen cards are selected without replacement from a well-shuffled pack of 52
playing cards.
The nine experiments, 3-11, have two common features.
(i) Each of these experiments hve more than one possibie outcome.

(ii) It is impossible to predict the outcome of the experiment.
For example, we cannot predict whether a coin, when it is tossed, will turn up a head or a tail
(Experiment 3). Can we predict without error the number of busy telephones (Experiment 7)?
It is impossible to predict the 13 cards we shall obtain from a well-shuffled pack (Experiment 11).
Do you agree that all the experiments 3-1 1 have the above-mentioned features (i) and (ii)?
Go through them carefully again, and convince yourself.

This discussion leads us to the following definition.
Definition 1 : An experiment with more than one possible outcome and whose result cannot be
predicted, is called a random experiment. Experiment

So, Experiments 3 to 11 are random experiments, while in Experiments 1 and 2 the outcome of
the experiment can be predicted. Therefore, Experiments 1 and 2 do not qualify as random
experiments. You will meet many more illustrations of random experiments in this and
subsequent units.

Note In the dictionary you will find that something that is random, happens or is
chosen without a definite plan. patteron or purpose.

1.2 Sample Space

In the previous section you have seen a number of examples of random experiments. The first
step we take in the study of such experiments is to specify the set of all possible outcomes of the
experiment under consideration.

When a coin is tossed (Experiment 3), either a head turns up or a tail turns up. We do not consider
the possibility of the coin standing on its edge or that of its rolling away out of I sight. Thus, the
set SZ of all possible outcomes consists of two elemends, Head and Tail. Therefore, we write SZ
= (Head, Tail) or, more simply, SZ = (H, T).

Note  is the Greek letter capital ‘omega’

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