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    I like the arguments for reframing the Bayes rule using odds, and the video is great (3b1b has some other awesome videos on Bayes theorem as well). Though the experiment (at 4:00) seems to indicate that the doctors in the seminar might not have been considering Bayes rule at all. I’d guess that those who answered incorrectly were just going with their intuition rather than thinking about how the low prevalence factored in. One of the comments on the video supports this idea:

    As a scientist who does medical tests, I’m amazed that any of the doctors asked got the right answer. Every doctor I work with assumes tests are 100% accurate.

    While I like the ideas presented here, I don’t know that redesigning Bayes rule alone would help – perhaps redesigning Bayes rule in addition to somehow making doctors more cognizant of Bayesian thinking when interpreting medical tests would help.