What is the probability that an Event A (which occurs 4 in 36) will occur 4 times before Event B (which occurs 10 in 36) occurs a 5th time ?
Consider the string $AAAABBBB\Large B$
The probability of that string occurs is $\displaystyle {\left( {\dfrac{4}{{36}}} \right)^4}{\left( {\dfrac{{10}}{{36}}} \right)^5}$.
However, how many ways can four A's & four B's appear before the $\Large B~?$