Optimum Chance

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

Answer:

The best way is to put one black ball in the first box, and all other balls in the second box. Then, the probability of grabbing a blackball from the first box is 1, and the probability of grabbing a black ball from the second box is 99/199. The total probability of grabbing a black ball is 0.5 × 1 + 0.5 × 99/199 = 298/398(approximately 74.9%).