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Rolling the Dice

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#26344
Fun:*** (2.83)
Difficulty:** (2.09)
Category:Probability
Submitted By:kissA****
Corrected By:Shadows

 

 

 



A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6.

The dealer says: "You can choose your bet on a number, any number from 1 to 6. Then I'll roll the 3 dice. If none show the number you bet, you'll lose $1. If one shows the number you bet, you'll win $1. If two or three dice show the number you bet, you'll win $3 or $5, respectively."

Is it a fair game?


Hint

What will happen if there are 6 gamblers, each of whom bet on a different number?
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