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A Problem With Pearls

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Fun: (2.83) Difficulty: (1.31) Category: Probability Submitted By: No_Eyed_Fsh

"I'm a very rich man, so I've decided to give you some of my fortune. Do you see this bag? I have 5001 pearls inside it. 2501 of them are white, and 2500 of them are black. No, I am not racist. I'll let you take out any number of pearls from the bag without looking. If you take out the same number of black and white pearls, I will reward you with a number of gold bars equivalent to the number of pearls you took."

How many pearls should you take out to give yourself a good number of gold bars while still retaining a good chance of actually getting them?

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