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>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>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>