Final answer:
A binomial probability distribution is used to model experimental probabilities when actual trials are not feasible, provided there is a fixed number of trials, only two possible outcomes, and the trials are independent and conducted under identical conditions.
Step-by-step explanation:
When conducting an experiment and real trials are not feasible, a mathematical model called the binomial probability distribution can be used to find experimental probabilities. This model applies in situations where the following conditions are met:
- There is a fixed number of trials.
- There are only two possible outcomes for each trial, typically called success and failure, where the probability of success is denoted by p and the probability of failure by q, with p + q = 1.
- The trials are independent and conducted under identical conditions.
The outcomes of such an experiment align with a binomial distribution, where the law of large numbers indicates that as the number of trials increases, the experimental probability (or relative frequency) approaches the theoretical probability.