SOLUTION: two standard dice are rolled. what are the odds against rolling a sum of 4 or 11?

Question 470231: two standard dice are rolled. what are the odds against rolling a sum of 4 or 11?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
In other words:
What are he odds in favor of rolling any sum EXCEPT
4 or 11?
Since there are 6 numbers of each die, there are
ways to get a result.
( odds against rolling 4 or 11) = ( odds in favor of getting ANY number) - ( odds in favor of getting 4 or 11 )
------------------------
Ways to get a 4:
1 and 3
3 and 1
2 and 2
Ways to get an 11:
4 and 7
7 and 4
5 and 6
6 and 5
So, there are 7 results you must avoid
Working with probabilities:
P(of getting ANY result) = 1
P(of getting 4 or 11) = 7/36
P(against rolling 4 or 11) = 1 - 7/36
1 - 7/36 = 36/36 - 7/36
1 = 7/36 = 29/36
To compute odds, it is (what you want):(what you don't want)
36 - 29 = 7 (what you don't want)
The odds against rolling 4 or 11 is 29:7
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