The probability below can be found by adding a few geometric probabilities.
Question
If a fair six-sided die is rolled repeatedly, what is the probability that it will take between 6 and 8 rolls (inclusive) to get the first "six"?
(Solved in full version)
Adding probabilities like this works provided there are not too many of them. However an alternative way to find probabilities is to use the cumulative distribution function.
Question
If a fair six-sided die is rolled repeatedly, what is the probability that it will take between 10 and 20 rolls (inclusive) to get the first "six"?
(Solved in full version)