dice rolling

Question

involving the rolling of two fair dice.
What is the probability of one of the dice showing 4 or the sum being at least 8?

Answer 1

to have one of the dice show a 4 you have the following possibilities:

41,14,42,24,43,34,44,45,54,46,64

for the sum to be at least 8, you have 5 8s, 4 9s, 3 10s, 2 11s, and 1 12

you can't repeat an outcome

there are only 4 8s because we already have 44

there are only 2 9s because we already have 45 and 54

there is only 1 10 because we already have 46 and 64

the total number of favorable outcomes is 11+4+2+1+2+1=21

the probability is 21/36=7/12