SOLUTION: Find the odds of rolling a pair of dice and getting a sum of 11 or greater

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Question 1053270: Find the odds of rolling a pair of dice and getting a sum of 11 or greater
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Find the odds of rolling a pair of dice and getting a sum
of 11 or greater
Here are all possible rolls:


(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)  

The rolls with sum 11 or greater are in red,
and the ones not with sum 11 or greater are
in blue.  The odds in favor of red are
"reds:blues".  We count the red ones.  There are
3.  We count the blue ones.  There are 33.
So the odds in favor are 3 to 33 or 3:33
and we can divide both by 3 and get 1:11, 
which is read as "1 to 11".  

[Note: If you had been asked for the odds against 
instead of the odds in favor, the odds against are 
33 to 3 or 33:3 and we can divide both by 3 and 
get 11:1, which is read as "11 to 1".

If you had been asked for the probability instead
of the odds in favor, the probability would be 3 out of 36,
or 3/36 which reduces to 1/12.]


Edwin

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