## Balls in a JarProbability puzzles require you to weigh all the possibilities and pick the most likely outcome.
You're walking down a street, when you see some people gambling on the roadside.
The dealer says: "There are 10 black balls and 10 white balls in this jar. You are blindfolded and you randomly pick 10 balls. If 5 of the balls you picked are black and the other 5 are white, you lose $2. Otherwise you win $1." Is the gamble fair? ## AnswerThe number of combinations to take 10 balls out of 20 is 20!/(10!)^2=184756.The number of combinations to take 5 balls of each color is (10!/(5!)^2)^2=63504. This means in 184756 games you lose 63504 games and win 121252 games in average, totaling a loss of $5756. In other words, you lose about $0.03116 per game in average. Therefore, the gamble is not fair. Hide ## What Next?
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