# Experimental Probability Examples

Experimental probability is defined as the probability of an event when ratio of occurrence of events and total number of trials is taken.

Example 1:

If a coin is tossed 10 times, head appears 3 times. Find experimental probability of getting a head.

Solution:

Experimental probability of getting a head = $\frac{3}{10}$.

Example 2:

If a dice is rolled 500 times and a 3 comes 313 times. What will be the experimental probability of 3 showing up in the dice?

Solution:

The total number of trials = 500.

Number of occurrences of where 3 will come = 313

Experimental probability of getting a 3 = $\frac{313}{500}$.

## Word Problems

Problem 1:

If a dice is thrown five times out of which thrice it gives a 4, then what will be the experimental probability of getting a four with a dice? Compare it with theoretical probability.

Solution:

Theoretical probability = $\frac{1}{6}$

Experimental probability = $\frac{4}{6}$ = $\frac{2}{3}$

The experimental probability gives the ratio of actual occurrence of events to number of possible events whereas theoretical probability gives the
expected probability of events.
Problem 2:

The given table gives the outcome when a coin is tossed 5 times. Find the experimental probability of getting a head.

 Trial1 Trial2 Trial3 Trial4 Trial5 Outcome H T T H T

Solution:

Number of occurrence giving a tail = 3

Total number of trials = 5

Experimental probability = $\frac{3}{5}$
Problem 3:

Annie has given GATE exam thrice and has not qualified even once. Find the theoretical and experimental probability of her qualifying the exam next time.

Solution:

Theoretical probability = $\frac{1}{2}$

Number of trials = 3

Number of trials giving qualified result = 0

Experimental probability = $\frac{0}{3}$ = $0$
Problem 4:

A coin is tossed 1000 times and head comes for 667 times. Find the experimental probability of getting a head.

Solution:

Number of trials = 1000

Trials giving head as outcome = 667

Experimental probability = $\frac{667}{1000}$
Problem 5:

A coin is tossed and a dice is rolled simultaneously for 6 times. The outcomes are given in the table below.

 Trail1 Trial2 Trial3 Trial4 Trial5 Trial6 Coin H H T T H T Dice 2 5 2 1 5 6

Find the experimental probability of getting a head and a five together.

Solution:

Number of trials = 6

Number of trials getting a head and a five = 2

Experimental probability = $\frac{2}{6}$ = $\frac{1}{3}$