What is the Difference Between Theoretical and Experimental Probability?

The main difference between theoretical and experimental probability lies in how they are determined:

• Theoretical probability is based on the underlying probability distribution of the experiment, which describes how likely an event is to occur. It is derived from knowledge and mathematical reasoning, and it represents the expected outcome if the experiment were repeated an infinite number of times. For example, the theoretical probability of getting heads when flipping a fair coin is 0.5 (1/2).
• Experimental probability is the actual outcome of an experiment, which describes how frequently an event actually occurred in a specific set of trials. It is an estimate of the theoretical probability, based on the results of a finite number of trials. For instance, if you flip a fair coin 100 times and get 46 heads, the experimental probability of getting heads in this specific experiment is 46/100 = 0.46 (or 46%).

Experimental probability can differ from theoretical probability due to the effects of chance. However, as the number of trials in an experiment increases, the experimental probability tends to converge towards the theoretical probability.

Comparative Table: Theoretical vs Experimental Probability

Theoretical and experimental probabilities are two different approaches to understanding the likelihood of an event occurring. Here is a table summarizing their differences:

In practice, experimental probability is used to estimate the true probability of an event based on actual observations, while theoretical probability is derived from mathematical reasoning and provides the expected probability of an event. However, there may be differences between the two probabilities due to various factors, such as the finite number of trials and unknown variables.