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The answer looks a bit simplistic compared to the question (as I interpreted it at least). In order to estimate the risk of incorrect ordering you have to calculate P(p2 > p1) where p1 and p2 are drawn from different beta distributions. AFAIK there’s no closed form expression for that probability (so Monte Carlo is one possible approach).

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The question doesn’t ask for that —- it explicitly asks us to control for over estimation of the fraction — although I rather like your interpretation as an extension.

Ok. I may have read a bit too much into this paragraph:

> Order the items above, smallest fraction first, whilst taking into account the uncertainty in the number of trials to bound the probability of over-estimating each fraction.

But why mention ordering if you’re not looking for statistical reasoning around the ordering in particular?

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