View Full Version : Attn newbies: the probablility-odds formula from Dr. Math

07-14-2003, 05:58 PM


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