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 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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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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