I hope the topic makes sense... I'm not well grounded in statistics.

Consider a set of m rolls with a chance p of rolling 1 and q of rolling 0. On a roll of 1, there is an additional chance that you will gain an additional roll, up to a total of n rolls. What are the individual probabilities of rolling 0-n? (Alternatively, the average total rolled should be sufficient)

Trying to keep it as general as possible as I may have to do this again, but the individual numbers are 5 initial rolls at p=0.935 and q=0.065, up to 8 rolls total, if you're feeling generous. Thank you for your assistance.