If I ask how many times will I get a five (face not sum) in two rolls the answer is 11 of the 36 combinations will contain a five.
What is the formula to calculate the 11 rolls which include a five? For two rolls you can list all 36 combinations and count them? But if it is 6, 7, or 8 rolls that is quite a bit of combinations to list.
This is somewhat similar to the following post: Probability of getting $5$ once in rolling a dice two times if...
One formula used was where you take the complement, ex 1 - (5/6)^n where n is the number of rolls.
But if the question is how many times will you roll a 5 in 8 rolls, what formula gives you that value? What formula gives you just the numerator? Thank you
The basic formula you need is the binomial distribution. The probability that you will get exactly $k$ fives in $n$ rolls is given by $\binom{n}{k}p^k(1-p)^{n-k}$, where $p=\frac{1}{6}$ is the probability of getting a five on one roll.