Comments Regarding Probability

Definition of Probability

We will limit our discussion of probability to the definition that a probability is the relative frequency of the occurrence of the event in the long run.

p(X) = Limit as n>>inf of (f(x)/f(T)}
The probability of event X, P(X) is
  • the number of times event X occurred (instead of other possibilities such as Y or Z); f(X)
  • divided by
  • the total number of times it could have occurred; f(T)
  • provided that the number of times it could have occurred is very very large; n -> (infinity sign)
Flip a coin 1,000 times. It comes up heads 480 times, tails 519 times, and lands on its edge once. What is the probably of the event "tails" when the coin is flipped? f(X) = 519
f(T) = 1000 (also known as "n")

P(X) = 519/100 = 0.519

But since n isn't infinitely large the value of 0.519 isn't really a probability.

Because we generally don't have an infinite number of trials to count, we never really have a probability. Instead we simply have a proportion. If I toss a coin 50 times and it comes up heads 23 times the probability is not (23/50) [or whatever the decimal value might be]--the number is only the relative frequency or proportion.

Probability values must be between 0.0 and 1.0. The limits are that X never occurs [P(X) = 0] or that it always occurs [P(X) = 1]. A lot of times people get sloppy and refer to probabilities as percentages, "The probability of precipitation is 30%." Just move the decimal to the left two places and drop the "%" sign if the sloppiness bothers you (as much as it does me).

Probability is Used Two Ways in Modern Science

© 2002 by BurrtonWoodruff. All rights reserved. Modified Sunday, March 25, 2007