# Experimental Probability

You and your 3 friends are playing a board game. It’s your turn to roll the die and to win the game you need a 5 on the dice. Now, is it possible that upon rolling the die you will get an exact 5? No, it is a matter of chance. We face multiple situations in real life where we have to take a chance or risk. Based on certain conditions, the chance of occurrence of a certain event can be easily predicted. In our day to day life, we are more familiar with the word ‘chance’ as compared to the word ‘probability’. In simple words, the chance of occurrence of a particular event is what we study in probability.

There are two approaches to study probability:

• Experimental Probability
• Theoretical Probability

### Experimental Probability:

Empirical probability or experimental probability is based on actual experiments and adequate recordings of the happening of events. To determine the occurrence of any event, a series of actual experiments are conducted. Experiments which do not have a fixed result are known as random experiments. The outcome of such experiments is uncertain. Random experiments are repeated multiple times to determine their likelihood. An experiment is repeated fixed number of times and each repetition is known as a trial.

Mathematically,

Experimental Probability = Number of times an event occurs / Total number of trials.

Let us understand the concept of experimental probability through examples.

Example: You asked your 3 friends Shakshi, Shreya and Ravi to toss a fair coin 15 times each in a row and the outcome of this experiment is given as below: Calculate the probability of occurrence of heads and tails.

Solution: The experimental probability for the occurrence of heads and tails in this experiment can be calculated as:

Experimental Probability of Occurrence of heads = Number of times head occurs/Number of times coin is tossed.

Experimental Probability of Occurrence of tails = Number of times tails occurs/Number of times coin is tossed. We observe that if the number of tosses of the coin increases then the probability of occurrence of heads or tails also approaches to 0.5.