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nerfhammer comments on binomial variance problem - Less Wrong
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Comments (14)
What's the name of the principle that variance increases further from 50%?
Not having memorized the formula for variance in binomial distributions, but intuiting that said principle was true, was my weaker reason for concluding B.
More saliently, the problem statement contains the gratuitous information that boys are a majority in program A. It's Kahneman and Tversky, for FSM's sake; therefore this information is used to mislead. Therefore, B.
Decreases! Note that there's zero variance when p = 0 versus non-zero variance when p = 0.5.
No principle, just the fact that the variance of the binomial distribution is p(1-p), which peaks at p=0.5.