Introductory Bayesian problems

Discuss the wikitag on this page. Here is the place to ask questions and propose changes.
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It's not clear to me why the concept of log odds is needed to answer this problem. Or rather I feel that it isn't, and that a much simpler explanation could be given, and that the concept of log odds is shoehorned in.

Maybe this should just be a link to https://arbital.com/p/1td/, with a "hover to get the answer" ? It's not clear for me why it isn't so, if it means the reader is expected to always read the full linked explanations, or if he's expected to just look up the answer.