What is Random Experiment in Probability?

Let us consider some examples from our daily lives to understand random experiments. We all are used to playing indoor games like ludo, where we roll dice to move according to the points. They do not have a fixed outcome. The die can have six different results when thrown. Such experiments performed randomly without knowing a specific outcome are called random experiments. A random experiment can have both desired and undesired results. These experiments have a wide array of utilisation in our daily life like weather forecasts, tosses of games, etc.

Conditions of a Random Experiment

Not all experiments are random experiments. They must show the following characteristics to be considered random experiments:

1. No fixed outcome: As seen in the case of throwing a dice, it has six different outcomes, which vary with every throw. So, a random experiment should have multiple results.
2. Non-deterministic result: By this, we mean that the result of the experiment should not be known beforehand. The results will be known only when output is given.

A Random Experiment in Probability

In probability, the random experiment is utilised to determine the frequency of a particular outcome amongst all the outcomes. For instance, we use the concept of probability to find out the frequency that the output will be 5 on rolling. Here, the total outcomes are either 1 or 2 or 3 or 4 or 5 or 6.

The formula for finding the probability of occurrence of a certain outcome is:

P (favourable outcome) = ((no of favourable outcomes)/ (total number of outcomes))

 An Example

As we have learned the concept of random experiment and seen its usage in probability using a certain formula, let us now solve a few numerical based on the mentioned formula.

 First, we will consider the experiment of finding out the factors of 36.

Here, all possible outcomes are {1,2,3,4,6,9,36}

1. What is the probability of the factor being 3?

Ans: P(factor is 3)= (number of times 3 occurs)/total number of outcomes))

     =⅕

2. What is the probability of the factor being 2?

Ans: P (factor is 2) = (number of times 2 occurs)/total number of outcomes))

     =⅕

3. What is the probability of the factor being 4?

Ans: P (factor is 4) = (number of times 4 occurs)/total number of outcomes))

     =⅕

4. What is the probability that the factor of 36 will be only 6?

Ans: P (factor is 6) = (number of times 6 occurs)/total number of outcomes))

     =⅕

5. What is the probability that the factor of 36 will be only 9?

Ans: P (factor is 9) = (number of times 9 occurs)/total number of outcomes))

     =⅕

Practice time! 

Now, let us experiment with finding out the factors of 300. Solve the below-given questionnaire for the above experiment to find the probability that:

1. The factor of 300 will be only 2?
2. The factor of 300 will be only 3?
3. The factor of 300 will be only 4?
4. The factor of 300 will be only 5?
5. The factor of 300 will be only 6?
6. The factor of 300 will be either 2 or 5?
7. The factor of 300 will be either 3 or 6?
8. The factor of 300 will be only 1?
9. The factor of 300 will be only 7?
10. The factor of 300 will be only 10?

Conclusion 

In this article, we studied what a random experiment is, learned about the conditions of a random experiment, and studied different examples of a random experiment. We also read about using random experiments in probability and the formula to determine the probability of certain outcomes.