How to find the probability of a dice roll

Question

2 dice are rolled and the numbers on the top faces are recorded. What is the probability that the sum of these numbers is at least 7?

Answer 1

there are 36 sums in the sample space

 

        1    2    3    4    5    6 

 

1      2    3    4    5    6    7

 

2      3    4    5    6    7    8

 

3      4    5    6    7    8    9

 

4      5    6    7    8    9    10

 

5      6    7    8    9   10   11

 

6      7    8    9   10  11   12

 

there are 6 7's, 5 8's, 4 9's, 3 10's, 2 11's 1 12 for a total of 21 numbers that are 7 or greater

the probability is 21/36=7/12