<p>Say you are a white male from a private school in New England:</p>

divide product by 50% for gender
divide product by 34% for school
divide product by 63.5% for race
divide product by 18.1% for geography
(divide product by ??? for alumni)</p>

<p>I get around 40 White males from Private schools in New England</p>

<p>(Not counting Almuni)</p>

<p>Also not dividing by sports</p>

<p>"I get around 40 White males from Private schools in New England"</p>

<p>That has to be false.</p>

<p>How about public school? And another question, is being from upstate NY as much as a disadvantage as being from NYC?</p>

<p>Your "analysis" assumes the variables are independent. They are not.</p>

<p>^ Good point. The events are not mutually exclusive and there is no way to know what the intersection between white and private school is.</p>

<p>
[quote]
Good point. The events are not mutually exclusive and there is no way to know what the intersection between white and private school is.

[/quote]
</p>

<p>Actually, the analysis of the OP does not assume the events are disjoint. That is not the problem with the analysis. The problem, as Leon correctly points out, is the assumption of independence.</p>

<p>Or between New England and private....</p>

<p>Lets make it simple</p>

<p>2102
divide by 34%</p>

<p>roughly 714 are private school</p>

<p>Agree?</p>

<p>I agree that 34% of 2102 is 714.68, but I do not agree that you have reliable information on the geographical (or ethnic) distribution of these 715 private school students.</p>

<p>Yes, that's correct. The probability of both events A and B being true is:</p>

<p>P(A ∩B) = P(A) * P(B | A)</p>

<p>And when the events are independent, as we usually assume for most situations, P(B | A) = P(B). It's strange that we intuitively multiply the probabilities of two events to determine the probability of both happening but never stop to think about the mathematical reasoning behind it.</p>

<p>It's also strange that we never think of the mathematical logic behind "divide by x%". Because if we did, we'd realize that dividing by 50% doubles the number, not halves it.</p>

<p>heheheh good point</p>