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Krasmaniandevil t1_j6ndhnx wrote

Reply to comment by Epic_Meow in TIL That the character who first said the phrase "fortune favours the bold" - Turnus, in the Aeneid, spends the rest of the story suffering military defeats before he's killed and heads to the underworld, miserable, at the end of the last book. by Equal_Caregiver_4909

That person would be lucky, but not very lucky. It's the whole "snatching victory from the jaws of defeat" angle that makes it.

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Epic_Meow t1_j6ngj2f wrote

but you're doing the same thing either way. unless their resume manages to catch your eye from the trash unexpectedly, maybe that's what you meant idk

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Dookie_-_Monster t1_j6nole0 wrote

The chance of picking one paper out of a stack is 1 / n (n is the number of papers).

The chance a piece of paper goes in the trash is 1/(.5n). The chance that piece is then picked out of the trash is then 1/(.5n) again. Multiply those and you get 1/(.25n^2).

So we can compare them to see if those are actually the same quantity.

1 / n < 1/(.25n^2)

n < .25n^2

4n < n^2

4 < n or n > 4

So if your stack has 4 or more pieces of paper in it, getting the paper out of the garbage is less likely (i.e. luckier) than just picking the paper out of the whole stack.

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Athildur t1_j6nyzqa wrote

So let's say...10 papers.

Chance of any one to be picked blindly: 1/10.

Chance any one is discarded into the trash: 5/10 (not 1/5 as you said, it should be .5n/n, or just 50%).

Chance for any one paper being picked out of the trash: 1/5 (since there are 5 in the trash).

1/5 of 5/10 is 1/10. Which is the chance we started with by just picking at random.

So no. Getting the paper out of the garbage isn't less likely at all in your example. The only factor not included here is the likeliness that one is picked from the trash at all. Since, if this were an uncommon event, it would make chances lower. But since this experiment presumes doing so is already predetermined (since you've built this selection method purposely), it adds no rarity or value.

In fact, since you premeditated this, arguably the stack in the trash is less lucky since you already decided at the start you'd pick one of those.

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