Probability math problem

Question

If two fair dice are rolled, find them probability that the sum of the dice is 8, given that the sum is greater than 6

Answer 1

the probability is the number of ways you can get 8 divided by the number of ways you can get 7 or more

possibilities are 7, 8, 9, 10, 11, and 12 for 2 dice, each with 1 to 6 as possible outcomes.

There's only 1 way to get 12, just 6 and 6

2 ways to get 11, 6 and 5 or 5 and 6

3 ways to get 10, 6 and 4, 4 and 6, or 5 and 5

4 ways to get 9, 6 and 3, 3 and 6, 5 and 4, 4 and 5

5 ways to get 8, 4 and 4, 5 and 3, 3 and 5, 6 and 2, 2 and 6

for 7, it's 4 and 3, 3 and 4, 5 and 2, 2 and 5, 6 and 1, 1 and 6

for 6 ways

total different ways are 1+2+3+4+5+6 = 21

sum of n numbers, 1 through n is (n)(n+1)/2 = 6(7)/2= 21

5 out of 21 are 8's

P(x=8/x>6)= 5/21 = about 0.2381, close to but less than 25% of the time