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## Game of Dice

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

 Puzzle ID: #17929 Fun: (2.42) Difficulty: (2.11) Category: Probability Submitted By: jmcleod Corrected By: Winner4600

Let's play a game: we'll roll two dice. If a 3 appears on either die, then we will pick them both up and re-roll them. If not, then we'll add them together. If the sum of the two dice is even, I win, and if the sum is odd, you win. What is the probability you'll win? What is the probability I'll win?

### Answer

The probability I'll win is 13/25
The probability you'll win is 12/25

There are 36 possibilities when rolling two dice, 18 odd and 18 even. 11 of those possibilities have a 3 involved on at least one die and are excluded in this game. Five of the excluded possibilities are even and six are odd. This leaves us with 13/25 probability of an even number and 12/25 probability of an odd number.

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