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Cong Chen
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Misunderstanding the chi squared distribution
Adding equivalent Python code as requested
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How important are confidence intervals?
AM-GM inequality means A is the better investment. :)
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Usefulness of the confidence interval
Well, you can calculate all the proportions for which the chance of seeing 1 black and 4 white sheep is greater than 5%. That would be all the "reasonable proportions" based on your observation. This is a 95% confidence interval. Is that true? I'm having a lot of trouble getting my head around the functorial definition and yours, which seems to be around conditional probability.