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Odds Slang for Probability?


Date: 02/06/97 at 15:44:00
From: Anonymous
Subject: Odds and probability

What is the difference between odds and probability? Or is odds a 
slang term for probability?


Date: 02/06/97 at 21:41:26
From: Doctor Wallace
Subject: Re: Odds and probability

No, odds is not slang for probability.  There is a difference.

A probability is a number from 0 to 1 inclusive, usually expressed as 
a fraction, which is the ratio of the number of chances of a specific 
event to the total number of chances possible.

For example, if I have 4 marbles in a jar, 3 red and 1 blue, then the 
probability of drawing the blue is 1/4.  There is one chance of a blue 
marble and 4 total chances (marbles).

Odds are expressed as the number of chances for (or against) versus 
the number of chances against (or for).  So, since there is 1 chance 
of your picking the blue, and 3 chances of your picking red, the odds 
are 3 to 1 AGAINST you picking the blue.  For odds in favor, we just 
reverse them.  The odds are 1 to 3 IN FAVOR OF you picking the blue.  

This can be a little confusing, so I'll say it again.  If you express 
odds as AGAINST, you put the number of chances against first, versus 
the number of chances for.  If you express odds as IN FAVOR OF, you 
put the chances for the event happening first.

Note that this does NOT mean that the probability is 1/3 for or 
against in the above example.

To convert odds to probability, we have to ADD the chances.  So, if 
the odds against a horse winning are 4 to 1, this means that, out of 
5 (4 + 1) chances, the horse has 1 chance of winning.  So the 
PROBABILITY of the horse winning is 1/5 or 20 percent.

I hope this helps.  If you need more assistance, don't hesitate to 
write back!

-Doctor Wallace,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Definitions
High School Probability
Middle School Definitions
Middle School Probability

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