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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?

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 jimbo Jun 16, 2004 Good teaser. It seems really odd that even would win! dumbell Jun 16, 2004 What Jimbo, even though you know odd would win, even then it seems odd? Drakar Jun 17, 2004 Well, you had an even chance of answering the odd teaser correctly, at least half of it. Good teaser! JessicaLynn Mar 03, 2005 I only found 21 possibilities. Where are the others? chuckelect Mar 07, 2005 nice teaser! Ms50cent Apr 17, 2005 I bet Ms50cent can do batter than dat. lessthanjake789 Jun 24, 2005 but one of the evens is 3 and 3, so wouldnt that get re rolled? Navyseal Aug 07, 2005 That was fun, but not too hard! Steve1973 Sep 22, 2005 Possible rolles.... 1st Dice is 1, 2nd dice is 1,2,4,5,6 Totals = 2, 3, 5, 6, 7 1st dice is 2, 2nd dice is 1,2,4,5,6 Totals = 3, 4, 6, 7, 8 1st dice is 4, 2nd dice is 1,2,4,5,6 Totals = 5, 6, 8, 9, 10 1st dice is 5, 2nd dice is 1,2,4,5,6 Totals = 6, 7, 9, 10, 11 1st dice is 6, 2nd dice is 1,2,4,5,6 Totals = 7, 8, 10, 11, 12 Add up the number of even totals: 2,6, 4,6,8,6,8,10,6,10,8,10,12 = 13 Add up the number of odd totals: 3,5,7,3,7,5,9,7,9,11,7,11 = 12 As you can see, there's 13/25 even numbers and 12/25 odd numbers. As you can see, the answer is correct. paul726 Feb 20, 2006 Very good teaser. And correct, I might add. brainjuice Mar 27, 2006 wew.. i didnt notice that there are two die. i thought that it is only one die which is rolled so my answer is, the probability i win is 1/3 the probability you win is 1/2 haha..nice teaser