Question

What is meant by empirical probabilities? Give an original example. What is meant by classical probabilities? Give an original example. How do these differ?

Answer 1

Empirical probability of an event is defined as the ratio of the number of outcomes in which a specific event occurs to the total number of trials.

Original example:

Suppose we toss a coin 4 times. Head appears only once.

Then, Empirical Probability of Head = 1/4

Classical probability of an event is a measure of the likelihood of the event happening. in theoretical sense.

Original example:

Suppose we roll a fair die.

Probability of getting the number 1 = 1/6, because all the numbers: 1,2,3,4, 5 or 6 are equally likely.

Thus, the empirical probability and classical probability differ in the basic principle that empirical probability is based on the actual outcome of an experimentation, whereas classical probability is purely theoretical in nature.