They *are* independent, conditional on Side Effects and Flu (aka, Flu Shot and Sore Throat are d-separated by {Side Effects, Flu}).
And that update switches the relative positions of P(sore-throat|flu-shot) and P(sore-throat|~flu-shot).
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P(S|F,X) > P(S|~F,X) P(S|F,~X) > P(S|~F,~X) P(F|S) > P(X|S) Observe S: infer F, ~X "S because F" Then observe ~F: infer X "S because ~F"
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this is one of my favorite sufjan songs
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