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Is it true? (Posted on 2016-05-02) Difficulty: 1 of 5
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)

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution Simpson's Paradox (spoiler) | Comment 1 of 2
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.

/************************************/

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
  Posted by Steve Herman on 2016-05-02 09:19:15

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