Bayes argued that we should accordingly judge it to be more probable that all the raffle tickets are winners than that half of them are, and in turn more probable that half of them are than that only one in a thousand is. Perhaps we had already intuited as much, but Bayes’s logic offers us the ability to quantify that intuition. All things being equal, we should imagine it to be exactly eight times likelier that all the tickets are winners than that half of them are—because the tickets we drew are exactly eight times likelier (100% versus one-in-eight) in that scenario. Likewise, it’s exactly
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