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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 5/6 chance someone is put onto the side rail (the one the trolley won't go down without interfering with it)
There's a 1/6 chance someone is put onto the main rail (the one the trolley WILL go down)
You're more likely to be on the side track if you're involved in this scenario, so if you wanna get hit you SHOULD try to flip it (if you're the one on the side track, it guarantees a hit. If you're one of the 10 people on the main, you have a 90% chance of having a dead switch and should try anyway)
Unless being tired at work is making me miss something
No, your math is wrong. The chance you're on the main track is actually twice as high. Imagine it like this: When all numbers 1-6 would come up once, there have been 10 people overall on the main track and only 5 people on the side track
But 9 of those people can't affect the outcome either way. So the chance that you're on the main track and can affect the outcome in a positive way by flipping the switch is only 1/15.
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