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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:*** (2.43)
Difficulty:** (2.07)
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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Comments

jimbo*au*
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*us*
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*us**
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!
Steve1973Aus*
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.
paul726Aus*
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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