dates, Alex may observe that the nicer ones are less handsome on average (and vice versa), even if these traits are uncorrelated in the general population. Note that this does not mean that men in the dating pool compare unfavorably with men in the population. On the contrary, Alex's selection criterion means that Alex has high standards. The average nice man that Alex dates is actually more handsome than the average man in the population (since even among nice men, the ugliest portion of the population is skipped). Berkson's negative correlation is an effect that arises within the dating pool: the rude men that Alex dates must have been even more handsome to qualify. Quantitative example As a quantitative example, suppose a collector has 1000 postage stamps, of which 300 are pretty and 100 are rare, with 30 being both pretty and rare. 30% of all his stamps are pretty and 10% of his pretty stamps are rare, so prettiness tells nothing about rarity. He puts the 370 stamps which are pretty or rare on display. Just over 27% of the stamps on display are rare (100/370), but still only 10%(30/300) of the pretty stamps are rare (and 100% of the 70 not-pretty stamps on display are rare). If an observer only considers stamps on display, they will observe a spurious negative relationship between prettiness and rarity as a result of the selection bias (that is, not-prettiness strongly indicates rarity in the display, but not in the total collection). Statement Two independent events become conditionally dependent given that at least one of them occurs. Symbolically: If , , and , then and hence . Event and event may or may not occur , a conditional probability, is the probability of observing event given that is true. Explanation: Event and are independent of each other is the probability of observing event given that and ( or ) occurs. This can also be written as Explanation: The probability of given both and ( or ) is smaller than the probability of given ( or ) In other words, given two independent events, if you consider only outcomes where at least one occurs, then they become conditionally dependent, as shown above. There's a simpler, more general argument: Given two events A and B with 0 < P(A) ≤ 1, we have 0 < P(A) ≤ P(A U B) ≤ 1. Multiplying both sides