"On the twin cities campus, the odds of being admitted are almost
seven times more favorable for asian students than for white students.
 Hispanic students are about five times and black students are about
three times more likely to be admitetd than white students."

This was a quote from an article in a newspaper report.  I have been
researching odds on the internet, but I still can't quite get a grasp
on the idea.  What would be the odds of a white student here, as
opposed to an asian, or black student?  And how does this differ from
the probability?

---

Clarification of Question by swimcrew-ga on 20 Jul 2005 06:55 PDT

later in the article it states, "84% of white applicants are
admitted".  How then would you find what the odds are for a white
student being admitted, as opposed to any other group?

This is my take on it. The concept of odds in this case is based on
the success rate of an application. If only 10 asian students apply,
and 7 are admitted, then the success rate of asian applicants is 70%.
If 100 white students apply and 10 are admitted, then the success rate
of white applicants is 10%. You can obviously see that the odds of an
asian gaining entry is 7 times more favourable.

However, let's say this school only has 20 seats. And the 3 remaining
are given to black students. Then the probability of of a white
student in this school is? 10 out of 20, or 50%. Therefore you can
see, while the odds of a white student being admitted is pretty small,
the odds of finding one on campus can be pretty large.

I hope it is fair to assume that the admissions policy is color-blind,
that it admits students on the basis of SAT scores, etc., etc. that
have nothing to do with ethnic background.

Thus the probability of any one applicant's being admitted should be
the same, regardless the ethnic background.

What the newspaper has written is a typical mistake:  reporting the
results of the color-blind admission process in terms that suggest
statistical odds for subgroups based on the numbers in the subgroups
of the total number of applicants.

Even though from year to year there may be some consistancy in these
"odds", they don't exist.

Granted, Asians seem to lay a greater emphasis on education than some
other groups, and as a result there seem to be (probably are) a
greater proportion (relative to the total population) of them admitted
to colleges, appearing on scholarship lists, etc.

But if on the basis of such a calculation of "odds", suddenly many
more Asians with weaker high school records started to apply to Twin
City, the proportion of  this larger subgroup that was admitted would
decline.

I'm sure you are aware...
Probabilities and odds say the same thing, in a little different
format. Odds are given as the quotient of (Probability of an Event
happening)/ (Probability of the event not happening.) Using that
formula.. a statement like  "3:1 odds" means x/(1-x)=3/1 (after the
algebra we discover) x=3/4 or 3:1 odds is equivalent to 75%
probability. So odds and probabilities are interchangable.

In the paragraph they aren't telling you the odds (or probabilities)
that any one of those groups has of being admitted. Basically they are
saying... "We know them, but we aren't telling you, and when we
compared them asians had 7 times better chances then whites... blacks
had three times etc...)

From that definition I gave you of odds.

Mr. White's odds. 
.84/.16 = 5.25
(When we talk odds we usually say this as some equiivalent whole
number fraction. in this case 21:4 -- its awkward, so i won't.)

So, if Mr. Asian's odds are 7 times larger, then his odds are 
5.25*7 = 36.75
x/(1-x)=36.75 implies x = .97 or 97%
Mr. or Ms. Black's odds are
x/(1-x)=3*5.25 --> 94%
Mr. or Ms. Hispanic's chances are
x/(1-x)=5*5.25  96%