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Sleeping Beauty Trolley Problem
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this post was submitted on 06 Nov 2023
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There's a 1/6 chance that scenario B happens, but that scenario involves 10 people, and the only thing you know is that you are one person strapped to the rail, so the chance that you are strapped to the main rail is P(main) = P(B|abducted) = P(abducted|B) * P(B) / P(abducted) = 10 * P(abducted|A) * 1/6 / P(abducted).
We can do the same for P(side) = P(A|abducted) = P(abducted|A) * P(A) / P(abducted) = P(abducted|A) * 5/6 / P(abducted). Then, P(main) / P(side) = 10 * 1/6 / 5/6 = 2. Since P(main) + P(side) = 1, then P(main) = 2/3 and P(side) = 1/3.
Edit: typo