What is the probability of rolling a sum of 10 with two dice?

Solution:

When two dice are rolled together then total outcomes are 36 and 
Sample space is 
[ (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) ]

So, pairs with sum 10 are (4,6) (5, 5) (6, 4) i.e. total 3 pairs

Total outcomes = 36
Favorable outcomes = 3

Probability of getting the sum of 10 = Favorable outcomes / Total outcomes

                                                        = 3 / 36 = 1/12

So, P(sum of 10) = 1/12