Explanation:
this is a combined event.
a probability is always the ratio
desired outcomes / totally possible outcomes
in our experiment with rolling 2 dice we have totally 6×6 = 36 different outcomes.
from these 36 total possibilities we desire the following (sum is less than or equal to 8, one die has to show a 6) :
6 1
6 2
1 6
2 6
that is 4 desired outcomes.
and the probabilty for this is
4/36 = 1/9 = 0.111111111...
in mathematical terms we could say :
one possible scenario is one die is 6, and the other is either 1 or 2.
the probability for one die to show 6 is
1/6
the probability for one die to show 1 or 2 is
2/6.
the probabilty for the combination is then
1/6 × 2/6 = 2/36 = 1/18
how many different combinations can we have ?
well, with 2 dice we have 2 such possible combinations.
therefore, the probability is
2 × 1/18 = 2/18 = 1/9.