I've searched through several questions trying to get the answer to this but been unable to find the answer I need. Most questions deal with consecutive results, but I am looking for non-consecutive results.
Basically, what is the formula needed to calculate the expected number of rolls needed to roll the number 6 n times. For instance, if a game requires me to roll the number 6 five times, how many times can I expect to roll the die before I get the result of 6 five times? They do not need to be consecutive.
To add difficulty to the problem, suppose I have a six sided die and a 10 sided die. What would be the formula to find the expected number of rolls to achieve a the number 6 five times on each die. You would roll both dice at once and record the results. If one die reaches the result five times before the other, it doesn't matter and you continue to roll both dice until each has achieved the result five times.
I'm still somewhat new to working out probabilities and having difficulty with this one.