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)
a=blonde, b=blue-eyed
The given statement is the conditional probability
P(a|b)>P(a)
Which by definition is
P(a and b)/P(b) > P(a)
A bit of manipulation gives
P(a and b)/P(a) > P(b)
Convert back to conditional probability
P(b|a)>P(b)
Which is the answer to the question: YES
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Posted by Jer
on 2016-05-02 09:19:38 |
Solution by formulas
