If the proportion of blonds among blue-eyed people is greater than among the population as a whole, is it also true that the proportion of blue-eyed people among blonds is greater than among the population as a whole?
Please justify your YES/NO answer.
(By A. Savin)
Yes.
Let a = # of blonde blue eyes
b = # of blonde non-blue eyes
c = # of non-blonde blue eyes
d = # of non-blonde non-blue eyes
Then a/(a+c) > (a+b)/(a+b+c+d)
Multiply by (a+c)/(a+b) to get
a/(a+b) > (a+c)/(a+b+c+d), and the YES is proven.
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I have been a little formal here, because intuition fails sometimes. See link to
Simpson's Paradox, which I always find counter-intuitive.
Edited on May 2, 2016, 9:19 am
Simpson's Paradox (spoiler)
