Theoretical vs Experimental Probability
Probability is the measure of expectation that a specific event will occur or a statement will be true. At all times, probability is given as a number between 0 and 1, where 1 and 0 imply that the event will definitely occur and the event will not occur respectively.
Determining the probability of an event is related to mathematics, and the branch of mathematics explaining the mechanism is known as the probability theory. It gives a mathematical foundation for developing advanced concepts of probability.
Experimental probability and theoretical probability are two aspects of probability, differentiated by the method of calculating the probability of an event. In experimental probability, the success and the failure of the concerned event are measured/counted in a selected sample and then the probability is calculated. In theoretical probability, a mathematical model is used to determine the behaviour responses to an event within the considered sample or the population.
Consider a bag containing 3 blue balls, 3 red balls, and 4 Yellow balls. If we calculate the probability of getting a red ball using probability theory, it is 3/10. From another perspective, if we draw balls from the bags and mark the colour and replace them, 3 out of 10 times a red ball will appear. But, if we do the experiment for 10 times the results may be different. It might give 5 times the yellow, 2 times the red and 3 times the blue ones, thus the result gives an experimental probability of 2/10 as the probability of getting a red ball.
The difference between the values obtained from the experiment and the theory is of a major concern when designing the statistical experiments. In theoretical probability, the ideal conditions are assumed, and the results are ideal values, but the deviation from ideal values in the experiment is due to the small sample size considered.
As the Law of Large Numbers states, the experimental values will get closer and closer to the theoretical value if the sample size is increased. This theorem was first stated by Jaco Bernoulli in AD 1713.
What is the difference between Theoretical and Experimental Probability?
• Experimental probability is the result of an experiment, and the theoretical probability is based on the mathematical model developed on the probability theory.
• The accuracy of the results of the experiments directly depends on sample size of the experiment and accuracy is greater when the sample size is greater.