What is the Difference Between Theoretical and Experimental Probability?

Theoretical probability relies on mathematical analysis, using the ratio of favorable outcomes to possible outcomes, whereas experimental probability is derived from observed outcomes in real-world trials.

Theoretical Probability:

Theoretical probability is based on mathematical analysis and relies on the assumption of equally likely outcomes in a sample space. It is calculated using the following formula:

P(E) = Number of Favorable Outcomes/Total Number of Possible Outcome

Where:

• P(E) is the probability of event E.
• The number of favorable outcomes is determined through mathematical reasoning.

Experimental Probability:

Experimental probability, on the other hand, is derived from actual observations or experiments. It involves conducting trials or experiments and recording the outcomes to determine the probability. The formula for experimental probability is:

P(E) = ​Number of Favorable Outcomes in Experiment/Total Number of Trials or Experiments

Where:

• P(E) is the experimental probability of event E.
• The number of favorable outcomes is observed through experimentation.