Question

Person x and Person y are playing a game. They each roll a die. Then they...

Person x and Person y are playing a game. They each roll a die. Then they subtract Person y's roll from person x's roll, and square the resulting number. Person y wins $5 if the results is 1,2,3, or 4. Person x wins $5 otherwise. Is this game fair? Explain using complete sentences.

Math   Statistics-And-Probability   
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Answer #1

If a die is rolled then the possible outcomes are 1,2,3,4,5 and 6.

If person X rolls a die the outcomes are 1,2,3,4,5 and 6 . It is same in the case of person Y.

Let z be the square of the subtracted number ie., Z =(Y-X)^2

Z takes the values of 0,1,4,9,16,25 and 36.

From the given data person Y wins $5 if the z value is 1,2,3 or 4

Person X wins $5 if the z value is 0,9,16,25 and 36

The probability of winning $5 is more for person X when compared to person Y as he can win only if he gets 1 or 4.

Therefore the game is not fair because person X has more chance of winning than that of person Y.

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