Defining Probability

Date: 4/30/96 at 21:42:22
From: Gary L Knox
Subject: Probability

We got into quite a disagreement and would like another qualified 
opinion.  It relates to the definition of probability.  Our text says 
the probability of an event is a number between 0 and 1.  One person 
thinks probabilities can be written only as a number from 0 to 1 like 
.732, etc.  Another person says probabilities may be written as 
percents.  

Our question... is a probability number equal to a percent?  
Is it correct to say the probability is 42 percent, the way they do on 
the weather, or are they using sloppy wording?

Gary

Date: 5/1/96 at 15:47:48
From: Doctor Ethan
Subject: Re: Probability

In my opinion, percents are a perfectly valid way to represent a 
probability.

In essence both probabilities and percents measure ratios of 
occurrences, and so they both seem like very natural ways to represent 
the same concepts.

In my experience, decimals are the most computationally efficient way 
to represent probabilities but I can think of cases where I would 
rather use fractions or percents.

I think that the biggest problem (and maybe this is big enough) is 
linguistic awkwardness.

Percents are usually used in a sentence like this:

  She got 93% of the answer right. 
  (This is not a probability measure.)

However, I think that we also might say

  She has a 93% chance of getting the next problem right.
  (This is a probability measure.)

So I guess I would say that although there may be a pedagogical reason 
to keep the notation distinct, these are in fact both ways of 
expressing ratios of values, and therefore could be used 
interchangeably with consistency.

-Doctor Ethan,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/