Experimental probability and theoretical probability are two different approaches to understanding and calculating probabilities.
Experimental Probability: Experimental probability is determined through empirical observation or direct experimentation. It involves conducting real-world experiments or simulations to collect data and then analyzing that data to calculate the probability of an event. Experimental probability is based on the observed frequency of an event occurring relative to the total number of trials or occurrences. For example, flipping a coin 100 times and recording the number of heads and tails to estimate the probability of getting heads.
Theoretical Probability: Theoretical probability, on the other hand, is based on mathematical calculations and reasoning rather than direct observation or experimentation. It is determined using theoretical principles and assumptions. Theoretical probability is often derived from a set of assumptions or known probabilities and involves using mathematical formulas to determine the likelihood of an event. For example, rolling a fair six-sided die and calculating the probability of rolling a specific number based on the assumption of equally likely outcomes.
In summary, experimental probability is based on observed data from experiments or simulations, while theoretical probability is based on mathematical calculations and assumptions. Experimental probability is more empirical and relies on real-world data, while theoretical probability is more deductive and uses mathematical principles to determine probabilities.