My intended correct answer is that, on this data, you technically can adjust your belief very slightly; but because the prior for a biased coin is so tiny, the update is not worth do
I would think that our prior for "health care improves health" should be quite a bit larger than the prior for a coin to be biased.
That depends on how long "we" have been reading Overcoming Bias.
Here's another installment of rationality quotes. The usual rules apply: