What is the probability of rolling a total of 7 with two dice at least once in 10 rolls?

When rolling 2 dice there are 36 possible outcomes.
[to see this imagine one die is red and the other green; there are 6 possible outcomes for the red die and for each of these red outcomes there are 6 possible green outcomes].

Of the 36 possible outcomes 6 have a total of 7:
#{color(red)1+color(green)6,color(red)2+color(green)5,color(red)3+color(green)4,color(red)4+color(green)3,color(red)5+color(green)2,color(red)6+color(green)1}#

That is #30# out of #36# outcomes will not be a 7 total.
#3/36=5/6#

We will not get a total of #7# on the first roll #5/6# of the time.

Of the #5/6# of the time we did not get a #7# on the first roll,
we will not get a #7# on the second roll #5/6# of the time.
That is #5/6xx5/6=(5/6)^2# of the time we will not get a total of #7# on either of he first two rolls.

Continuing with this reasoning, we see that we will not get a total of #7# on any of the first #10# rolls #(5/6)^10# of the time.

With the help of a calculator we find that we will not get a total of #7# on any of the first #10# rolls approximately #16.15%# of the time.

This implies that we will get a total of #7# on at least one of the first #10# rolls #100%-16.15%=83.85%# of the time.