Probability is the ratio of the total outcomes in an experiment to the number of outcomes that are favorable to the event of which we are finding the probability of. It is important that the event must always be associated to the experiment being talked about. For example: finding the probability of getting a 2 in the experiment of tossing a coin is not possible. The probability of the given event can only be found in the event of throwing a dice. Probability is always lying in the closed interval of 0 and 1, that is, [0, 1]. When then probability is 0 we call the event impossible to happen and when the probability is equal to 1, we call the event to be sure to happen.

There are two types of probabilities we talk about: theoretical and experimental. In theoretical probability we follow the formula as it is as given by the definition of the probability. That is, we divide the number of outcomes that are favorable to the event by the total number of outcomes in order to obtain the event’s probability.

## Experimental Probability Definition

In case of experimental probability we rely more on what we have actually done or performed live rather than as taken on paper via theory. Due to this we change the formula on the same basis. So we define experimental probability as the ratio of the number of occurrences of the event to that of the number of trials of the experiment being done.

We basically calculate experimental probability for a larger number of trials like 200 times a coin is tossed and so for more and more accuracy. In case of theoretical probability we basically take fair chances of all the outcomes as per the given conditions which are not an actual case. Basically, when we perform an experiment no event is equally likely to happen. For example: it is not necessary that in 3 trials we will get a single tail. But we consider that chance in case of theoretical probability. But in case of experimental probability we are actually calculating on the basis of the observations we have made by performing the experiment live.

## How to do Experimental Probability

At times we call experimental probability also as relative frequency because of its definition. For finding out experimental probability we first record the observations from all the trials we have made.

Then we found out how many times the given event has actually occurred in all the trials. Next we find the ratio of the number of occurrences of the event to the number of trial we have made. This gives us the experimental probability of an event.

It is important that we perform the experiment live and also the exact number of times as required or mentioned for finding out the experimental probability of an event. Also, the experimental probability may vary with every time the experiment is being performed. This is because the observations may vary each time we perform the experiment. This happens as nothing is predictable in real life and also events and the outcomes vary in real life as expected.

So every time we perform an experiment it is not at all necessary to get the same probability for an event after the experiment is completed and calculations are made.

## Experimental Probability Examples

Let us see an example on the basis of experimental probability for understanding it better.
Example:

We are given the marks of a 100 students obtained in a certain examination.

 Marks 10-20 20-40 40-60 60-80 80-100 No.of Students 5 15 35 30 15

Find the probability that when we select a student at random, the marks of the student are:
(a) Under 40
(b) Above 60
(c) Between 20 and 80
(d) The student gets a distinction.

Solution:

We know that experimental probability is the ratio of the number of occurrences of an event to the number of trials being made in an experiment.

(a) The number of students getting marks under 40 is 5 + 15 = 20

Therefore, probability of marks of student under $40$ = $\frac{20}{100}$ = $\frac{1}{5}$

(b) The number of students getting marks above 60 is 30 + 15 = 45

Therefore, probability of marks of student above $60$ = $\frac{45}{100}$ = $\frac{9}{20}$

(c) The number of students getting marks between 20 and 80 is 15 + 35 + 30 = 80

Therefore, probability of marks of student between $20$ and $80$ = $\frac{80}{100}$ = $\frac{4}{5}$

(d) The percentage for distinction is above 75% which we cannot determine according to the given data as some students of this range may also lie in the marks interval of 60 – 80. So we cannot actually determine in this case the number of students getting distinction without some more of the information being provided.