Answer to Question #38437 in Statistics and Probability for Maltesers

Question

So I had this Probability Question in class, and I didn't understand how my teacher got that answer.

So the Question is:
Two fair dice is rolled 'n' times. Find the probability of obtaining a double six 'at least once'.

How I answered the question was that, if we want a Double six at least once (which means getting a Double six, any number of times, be it once, twice, thrice....n times)

So the complement of that would be not getting a double six at all
And the P(Not getting a double six at all) = 35/36

so the P(Getting a double six at least once) = 1 - P(Not getting a double six at all)
P(Getting a double six at least once) = 1 - 35/36 = 1/36

So the Probability of getting a Double Six at least once (n times) = (1/36)*(1/36)*(1/36)....n times
P(getting a Double Six at least once (n times)) = (1/36)^n

but my teacher said that the answer is = 1 - (35/36)^n

Now, I didn't understand the logic she applied so please please can you please solve this and tell me if my answer is right or explain how is my teacher's answer right! Please, this Questions has been eating my head!