Protagoras comments on binomial variance problem - Less Wrong
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Comments (14)
Um, B, but only by a hair. 55 is equidistant between 45 and 65, but the variance is smaller for A because 65 is farther from 50 than 45 is, so measured by the relevant standard deviations, 55 is closer to 45 than 65. (Making the obviously obvious assumption that children are assigned to classes independent of gender.)
I had to google up the source to find out why the "obvious" answer is supposed to be A.
It looks like I approached the problem in exactly the same way you did. I'm very curious as to how common it is for people to think A is more likely; it really doesn't seem obvious to me either.
75% choose program A