Empirical and Mathematical Probabilities

Date: 12/04/98 at 15:16:23
From: Kristin M. Dettman
Subject: Probability

What is the difference between experimental probability and 
mathematical probability?

Date: 12/04/98 at 16:45:02
From: Doctor Bill
Subject: Re: Probability

Kristin,

I don't know what "experimental" probability is, but I think you might 
mean "empirical" probability.

Empirical probability means that you don't know anything about how an 
event behaves, i.e. what are the number of possible outcomes and what 
are the number of possible successes. So to find the probability of an 
event, you have to do the experiment many times to get an idea, or look 
at some data related to the event. As an example: "How much longer will 
a man who is 50 years old live?" There is no way to know the answer to 
this question without looking at a mortality table and noting the ages 
of men who have died, and drawing some conclusion from those data. This 
is called empirical (or posteriori) probability.

Mathematical (or priori) probability is based on the fact that you know 
the number of possible outcomes and the number of possible successes. 
For example, flip a coin. What is the probability of a head? You know 
it is 1/2 because you know the number of possible outcomes and the 
number of successes. Roll a die. What is the probability of a 4? You 
know it is 1/6 because you know there are 6 possible outcomes and only 
1 possible success. These results are based on mathematical 
probability. 

- Doctor Bill, The Math Forum
  http://mathforum.org/dr.math/