SOLUTION: What is the probability of not rolling a sum of 10 with two fair​ dice?

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Question 1100704: What is the probability of not rolling a sum of 10 with two fair​ dice?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming each die has 6 sides (labeled 1 through 6).

Let's make one die be red and the other be blue.

Make a table of all the possible sums that we can make (sums are in black ink)



There are 6*6 = 36 sums in the table. Of which, there are 3 copies of 10 (formed by 4+6=10,5+5=10,6+4=10). So that makes 36-3 = 33 copies that are not a sum of 10.

Divide the number of copies that aren't ten (33) over the total number of sums (36) to get 33%2F36+=+11%2F12. Don't forget to reduce as much as possible.

The answer as a fraction is 11%2F12

If you need the answer in decimal form, then use a calculator to get this approximate result 11%2F12=0.9167 (rounded to 4 decimal places)