Random Experiment

We engage in a variety of activities every day, often performing the same activities and getting the same or different results. Any experiment which can be repeated has a well-defined set of guidelines, and can have more than one outcome is called a random experiment. 

Here are some examples to understand random experiments:

●  Mathematically, the sum of all interior angles of a certain quadrilateral is 360 degrees, although we do not know the quadrilateral type or each interior angle.

●  We may undertake a number of scientific tests with different findings despite being repeated multiple times under uniform conditions.

●  A coin tossed may land a head or tail, but we have no way of knowing.

What is a random experiment?

In probability theory, an experiment or trial is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.A random experiment can have one or many outcomes.

Using the notion of a random experiment as a guideline,  we can tell whether or not the experiment is random by looking at the results. Here are some examples to help grasp what is meant by “random experiment” and what is not meant by “random experiment.”

Example 1: Is choosing a card from a properly shuffled deck of cards a random experiment?

Solution:

A deck of cards has 52 cards. Each of these cards has an equal possibility of getting picked.

• This experiment may be repeated multiple times and there are 52 potential results.
• Given that it is totally possible to choose any card from the deck, it is impossible to foresee the result beforehand.

The experiment satisfies both conditions stated above of being a random experiment.

    As a result, it is a completely random experiment.

Example 2: Is dividing 30 by 5 a random experiment?

Solution:

• One can repeat this experiment multiple times but the result will be the same every time.
• It is possible to predict the outcome of this experiment no matter how many times it is repeated. The result will always be 6.
• Therefore, this is not a random experiment.

Examples of random experiments

Some instances of random experiments and sample space are shown below.

The act of tossing a coin twice

The number of conceivable outcomes = 4

Example of a space = S = {HH, HT, TH, TT}

Choosing one of the factors of 180

Number of possible outcomes = 18

Sample space = S = {1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180}

Three coins are hurled in a row at the same time.

The number of conceivable outcomes. = 8

Sample space = S = {HHT, HHH, TTT, HTH, TTH, THH, THT, HTT}

Rolling a pair of dice simultaneously

The number of conceivable outcomes = 36

Sample space = S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Throwing a dice two times

Number of possible outcomes = 36

Sample space = S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Selecting a card from an urn containing 50 cards numbering from 1 to 50

Number of possible outcomes = 50

Sample space = S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,….., 45,46,47,48,49,50}

Probability experiments at random

An experiment is any action that produces an effect or a result. When doing an experiment or an activity, there is uncertainty about which one could occur. Experiments generally yield a variety of results. In any case, a random experiment is one that meets the two characteristics listed below.

• When there is greater than one probable conclusion from an experiment.

• When it is impossible to foresee the result ahead of time.

Conclusion

In conclusion,in the above article we learnt about what are random experiments and conditions to call an experiment random.In our daily life also we have to take certain risks or chances whose outcome we don’t know. The variable which is used to measure the outcome of the random experiment is called a random variable. The chance of probability being distributed over the random variables is called a probability distribution. The exact values are taken into account in the case of the discrete random variable, wherein continuous random variable the value falls in between intervals.