I am confused as to why anyone would not flip the switch? Flipping the switch seems to have somewhere between a 10% and 100% chance of saving your life, and not flipping the switch seems to guarantee death?
Is there some kind of penalty to flipping the switch that I am missing?
Or is the drawing misleading, and in Scenario B, there is also supposed to be a person drawn on the other track?
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
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.
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.
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