# Examples showing necessity and advantage of emperical definition of probability

As the title, I want to ask for some examples showing necessity and advantage of emperical definition of probability in teaching high school students.

We knew that the classical definition has some disadvantages, i.e, the sample space has to be finite and all cases are equally possible. Those are motivations for mathematicians to come up with the emperical definition. I would like to know some simple examples (to teach high school students) which we cannot apply the classical definition to calculate the probability.

Thank you very much.

• It seems odd to me that people feel that probability should be a defined term. There doesn't seem to be any problem that needs to be solved and that is solved by these definitions. – Ben Crowell May 6 '17 at 22:53
• What do you mean by the "empirical definition of probability"? Something like this? If so I'm not sure I understand the question, since empirical probabilities are the results of experiments, and can (basically) never be calculated theoretically. – user797 May 8 '17 at 22:20
• If you're just looking for something where the equiprobable model doesn't work, consider flipping a biased coin. (I'd give this as an answer, but I'm not sure it actually answers what you want to know) – user797 May 8 '17 at 22:21