If the proportion of blonds among blueeyed people is greater than among the population as a whole, is it also true that the proportion of blueeyed people among blonds is greater than among the population as a whole?
Please justify your YES/NO answer.
(By A. Savin)
a=blonde, b=blueeyed
The given statement is the conditional probability
P(ab)>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(ba)>P(b)
Which is the answer to the question: YES

Posted by Jer
on 20160502 09:19:38 