# EXPERIMENTAL PROBABILITY

Experimental probability refers to the probability of an event occurring when an experiment was conducted.

In such a case, the probability of an event is being determined through an actual experiment.

Example :

When we toss a coin 10 times, how many times can we get head ?

When we toss a coin once, the probability of getting head is 1/2.

Since, there is 50% chance of getting head when a coin is tossed once, we can say that we will get head 5 times out of tossing a coin 10 times.

Are we 100% sure that we will get head 5 times ?

When the actual experiment is conducted, the result may vary.

We may get head 0 times or 1 time or 2 times or 3 times ..........up to 10 times.

In the actual experiment of tossing a coin 10 times, say, we get head 3 times.

Then the probability of getting head is 3/10.

This is called experimental probability.

Because, here we find the probability after the experiment was conducted.

Based on the example explained above, we can get the formula given below to find experimental probability.

## Practice Questions

Question 1 :

David tossed a coin 20 times and received head 12 times and tail 8 times. Find the experimental probability of getting tail.

Step 1 :

Find the total no. of trials.

Total number of trials  =  20

Step 2 :

Find the no. of times tail received.

Number of times tail received  =  8

Step 3 :

Find the probability.

Experimental probability  =  8/20

Simplify.

Experimental probability  =  2/5

Question 2 :

A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table. What is the experimental probability that the next patient will be female and in the age range 22–39 ?

Step 1 :

Find the total no. of patients.

Total no. of patients is

=  44 + 66 + 32 + 53 + 36 + 50 + 45 + 74

=  400

Step 2 :

Find the no. of female patients in the age range 22 - 39.

No. of female patients in the age range 22 - 39  =  50

Step 3 :

Find the probability.

Experimental probability  =  50/400

Simplify.

Experimental probability  =  1/8

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