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September 17, 2015

A Probability Problem With Pearls

"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?

3 comments:

Shivraj Gawde said...

I'll take 5000 pearls,and the probability of having the same number of black and white pearls is 0.5.

Possibility 1: 2501 white and 2499 black
Possibility 2: 2500 white and 2500 black

Josh D. said...

Take out 5000 Pearls. There is only one left. If it's black, you win nothing, but if it's white you win 5000 gold bars.

revolver said...

Take out 4999. Draw one more. The probability of winning is 1/2.

Explanation: The last 2 pearls will be either WW, BW, or BB. If WW, drawing either pearl wins. If BW, B wins, W loses. If BB, both lose. So it's 3 wins to 3 losses, even odds.