You are kidnapped and your offender plays a game with you. In front of you are 2 boxes, containing a total of 50 white balls and 50 black balls. The kidnapper will pull out a ball from one of the two boxes, at random. If the ball is white you survive, if not, you are shot.
- Every ball must be in one of the boxes.
- No balls can be left out.
- Each box must have at least one ball.
Box 1: 25 black balls and 25 white balls Box 2: 25 black balls and 25 white balls.
In this example the chance to live is obviously $50 \% $. How can you distribute the balls so as to increase that chance?
Answer
Box 1: 50 black balls, 49 white balls Box 2: 0 black balls, 1 white ball.
In this example the chance to live is obviously $50\%+50\%*49/99 \approx 75\%$. There is no way to increase that chance.
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