"Suppose u think you're 80% likely to have left a power adapter somewhere inside a case with 4 otherwise-identical compartments. You check 3 compartments without finding your adapter. What's the probability that the adapter is inside the remaining compartment?" -
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20%, right? Without checking any compartments, each compartment has a 20% chance of having it
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Called it
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Replying to @JimDMiller and @ESYudkowsky
I think 80% is the midwit bait
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20%
if there's an 80% chance you have it, that means there's a 20% chance it's in compartment A, 20% in B, 20% in C, and then 20% in D
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Good one - answer is 50%. Dividing 80 by 4 means there's a 20% likelihood of the charger being in each compartment. The likelihood it's in the fourth compartment is 20%, equal to the likelihood it's not in the case.
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There’s a 100% chance it’s in the case but also 100% chance it’s not in the case. Shroedingers power adapter!
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Just apply Bayes rule.
Let A = you left the power adapter in the case and B = it's not in the 3 compartments you checked.
This means we are looking for P(A|B) = P(B|A)*P(A)/P(B) = .25*.8 / (.25*.8 + 1*.2) = 50%
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Other, I'd perhaps adjust down my prior of 80% after not finding it in the first three. (Consider a case with 100 compartments, if you eliminate 99 are you still as confident/consider an 80% chance of being in the case & therefore the final compartment as you were at the start?)
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