The document describes a dice game between Muhammed and Aly where Muhammed wins if the first die is a factor of the second, and Aly wins if one die is even and the other is odd. It calculates the chances of each player winning based on the possible die roll combinations, finding Aly has a 36% chance of winning compared to Muhammed's 28% chance, with a 36% chance of a tie. The document concludes the game is unfair and apologizes to Muhammed.

1. Pair-a-Dice
by Max Glaser, Nicholas Man andAlvin Tse
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2. Dice Game!
Muhammed wins if the number of the first die (with
numbers 1-6) is a factor of the second die (with numbers
7-12).
A%y wins if one is an odd number and the other is even.
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3. Muhammed’s chances
(1,7)(1,8)(1,9)(1,10)(1,11)(1,12)
(2,8)(2,10)(2,12)
(3,9)(3,12)
(4,8)(4,12)
(5,10)
(6,12)
15 chances of him winning
(5 chances of them both winning)
= 10 chances of him winning
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4. Ally’s chances
(1,8)(1,10)(1,12)
(2,7)(2,9)(2,11)
(3,8)(3,10)(3,12)
(4,7)(4,9)(4,11)
(5,8)(5,10)(5,12)
(6,7)(6,9)(6,11)
18 chances of her winning
(5 chances of them both winning)
= 13 chances of her winning
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5. Both losing numbers
(3,7), (3,11)
(4,10)
(5,7)(5,9)(5,11)
(6,8)(6,10)
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6. So...
The chance of Muhammed winning is 10/36 = 28%
The chance ofA%y winning is 13/36 = 36%
The chance of a tie is 13/36 = 36%
The game is not fair :(
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7. The end
And sorry Muhammed
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