# Random Experiments

When we perform experiments in science and engineering, repeatedly under very nearly identical conditions, we get almost the same result. Such experiments are called deterministic experiments. For example, given any cyclic quadrilateral, without knowing the angles we can say that, the opposite angles are supplementary.In any cyclic quadrilateral ABCD we have âˆ A + âˆ C = 180Â° and âˆ B + âˆ D = 180Â°.

Such experiments are called deterministic experiments.

There also exist experiments in which the result may not be essentially the same even if the experiment is performed under very nearly identical conditions. Such experiments are called random experiments. If we toss a coin, we may get 'head' or 'tail'.

**Toss a coin and you will get**

**head (H) or tail (T)**

**1 2 3 4 5 or 6**

An experiment is called a random experiment if it satisfies the following two conditions:

- It has more than one possible outcome.
- It is not possible to predict the outcome in advance.

# Sample Space

The**sample space**of a random experiment is defined as the set of all possible outcomes of the experiment. The possible outcomes are called sample points. The sample space is generally denoted by the letter S. We list the sample space of some random experiments.

Random Experiment |
Sample Space |

1. Tossing of an unbiased coin |
S = {H, T} |

2. Tossing of unbiased coin twice |
S ={HH, HT, TH, TT} |

Here, H is the head and T the tail. When two unbiased coin are tossed we get the following outcomes.

**HH **

**HT**

**TH**

**TT
**

**Example**

A bag contains 4 identical red balls and 4 identical black balls. The random experiment consists of drawing one ball, then putting it back into the bag and again drawing a ball. What are the possible outcomes of this experiment?

**Solution**

Let R and B represent a red ball and a black ball respectively.

S = {RR, RB, BR, BB}.