### Brain Teasers

# A Problem With Pearls

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

"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?

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?

### Hint

If you took out 2 pearls, you would have about a 50% chance of getting 2 gold bars. However, you can take even more pearls and still retain the 50% chance.### Answer

Take out 5000 pearls. If the remaining pearl is white, then you've won 5000 gold bars!Hide Hint Show Hint Hide Answer Show Answer

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## Comments

'no I a not racist.' LOL

This teaser was used in my recent WTB game, The Riddle Shop. No, it is not a riddle.

easy................ if that was me, i would have been sooooooooooooooooooooooooo rich!!!!!

great teaser!

The proposed answer assumes that one would rather have a 50% chance of winning 5000 gold bars than a 50.02% chance of winning a single gold bar. That's an accurate assumption in my case, but it does mean this isn't purely a probability problem.

Let's tweak the problem slightly. Keep the reward the same--one gold bar per pearl withdrawn. But let's add in a penalty. If you don't withdraw an equal number of black and white pearls, you die. In that case, I'd suggest withdrawing two pearls since that would (very slightly) increase your chance of remaining alive.

Let's tweak the problem slightly. Keep the reward the same--one gold bar per pearl withdrawn. But let's add in a penalty. If you don't withdraw an equal number of black and white pearls, you die. In that case, I'd suggest withdrawing two pearls since that would (very slightly) increase your chance of remaining alive.

The answer is not strict math proved.

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