Negative binomial distribution example

Question

I apologize if this is too simple a question. One of the exercises in my probability textbook says

"A dice is rolled until the first time T that a 6 appears. Find P(T > 3)"

The answer given is (5/6)^3. I am fairly certain this question is a negative binomial distribution question, because it is counting the number of trials until the first success, but I am unsure how the author arrived at this answer / what to plug in.

Thanks for the help!

Answer 1

The probability that we are rolling more then 3 times is actually the probability that 3 times we didnt got 6 in the dice, (since once we get 6 in the dice we are stopping).

now the probability of not getting 6, 3 times it's just (5/6)^3, since the probability of getting 6 is 1/6, so not getting 6 is 1-1/6=5/6 and to get it 3 time in a row it's (5/6)^3 since it's all unrelated.