Game of Dice
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
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 reroll 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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Comments
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 
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