# What was the best way in which the prince could divide the pearls over the vases?

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Long ago, a young Chinese prince wanted to marry a Mandarin's daughter. The Mandarin decided to test the prince. He gave the prince two empty, porcelain vases, 100 white pearls, and 100 black pearls. "You must put all the pearls in the vases", he told the prince. "After this, I will call my daughter from the room next door. She will take a random pearl from one of the two vases. If this pearl is a black one, you are allowed to marry my daughter."What was the best way in which the prince could divide the pearls over the vases?

posted Apr 30, 2014

## 1 Solution

+1 vote

put one black pearl in the first vase and all other pearls in the second vase. Then, the probability of grabbing a black pearl from the first vase is 1, and the probability of grabbing a black pearl from the second vase is 99/199. The total probability of grabbing a black pearl is 0.5 × 1 + 0.5 × 99/199 = 298/398 (approximately 74.9%).

solution May 6, 2014

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