Even though this account is new because it was created a few days ago with the server I've set up (lemmy.cat), I've been on Lemmy for a while and have contributed to its development (documentation and translation).
I'd love to be able to help moderate one of the most important communities, not only in terms of the number of people, but also in terms of what it represents.
You could try blacksmithing, people will pay well for a finely made knife. If you like horses and don't mind how scary they are you could get into farriering with the horseshoes you make. But then we're talking more of a job than a hobby.
You could try blacksmithing, people will pay well for a finely made knife. If you like horses and don't mind how scary they are you could get into farriering with the horseshoes you make. But then we're talking more of a job than a hobby.
ka = the potential prize in box B; i.e. "k times larger than a"
p = the odds of a false positive. That is, the odds that you pick box B only and it got nothing, because dumb machine assumed that you’d pick A too.
n = the odds of a false negative. That is, the odds that you pick A+B and you get the prize in B, because the machine thought that you wouldn’t pick A.
So the output table for all your choices would be:
pick nothing: 0
pick A: a
pick B: (1-p)ka
pick A+B: a + nka
Alternative 4 supersedes 1 and 2, so the only real choice is between 3 (pick B) or 4 (pick A+B).
You should pick A+B if a + nka > (1-p)ka. This is a bit messy, so let’s say that the odds of a false positive are the same as the odds of a false negative; that is, n=p. So we can simplify the inequation into
a + nka > (1-n)ka // subbing “p” with "n"
1 + nk > (1-n)k // divided everything by a
1 + nk - (1-n)k > 0 // changed sides of a term
1 + 2nk -k > 0 // some cleaning
n > (k-1)/2k // isolating the junk constant
In OP’s example, k=1000, so n > (1000-1)/(2*1000) → n > 999/2000 → n > 49.95%.
So you should always pick B. And additionally, pick A if the odds that the machine is wrong are higher than 49.95%; otherwise just B.
Note that 49.95% is really close to 50% (a coin toss), so we’re actually dealing with a machine that can actually predict the future somewhat reliably, n should be way lower, so you’re probably better off picking B and ignoring A.
asklemmy
Active
This magazine is from a federated server and may be incomplete. Browse more on the original instance.