Random Experiments

Random experiments are also known as observations. The word
‘Probability’ is used very often in our daily life; such as ‘probably he is an
honest man’, ‘what is the probability of a double head in a throw of a pair of
coin?’, ‘probably it will rain in the evening’ and so on.

These days, an attempt towards a theory of probability is extensively used in various fields of what we are interested in. The instant answer is obviously an event. At first we will discuss about the precise meaning of the term ‘event’ and how it is used in our mathematical theory. Now our next step will help us to get the idea of what are random experiments or observations.

Definition of random experiment:

An experiment for which we know the set of all different results but it is not possible to predict which one of the set will occur at any particular execution of the experiment is called a random experiment.

For example: tossing a fair coin, casting an unbiased die and drawing a card from a pack of 52 cards.

Let us take the experiment of tossing a coin. If we toss a
coin then we get two possible outcomes either a ‘head’ (H) or a ‘tail’ (T), and it is
impossible to predict whether the result of a toss will be a ‘head’ or ‘tail’.

Let us consider a similar experiment rolling a die from a
box. It we a die then there are only six possible outcomes. The faces of the
die are marked as 1, 2, 3, 4, 5 and 6 and these are the only possible outcomes.
But here also the outcome of a particular throw is completely unpredictable.

Again similarly when we are concerned about the
measurement of a chemical quantity with the required instrument the outcome of
the experiment does not exactly give the true value of the quantity but a value
close to it due to that are called experimental errors. If repeated
observations are taken the measured values are not again the same to the previous
one but it will fluctuate in an unpredictable manner. Here we can take, at
least for the theoretical considerations that the possible outcomes comprise
all the real numbers, but the number given by a single measurement can’t be
exactly predicted. In our mathematical theory we will only consider the
experiments or observations, for which we know a priori the set of all different
possible outcomes, such that it is impossible to predict which particular
outcome will occur at any particular performance of the experiment, are called
random experiments. As such, if a random experiment is repeated under identical
conditions the outcomes or results may vary or fluctuate at random.