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

<p>2102 total admits
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>
[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>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>