Let's say I have a fair coin and a fair die. If I flip the coin and get heads, I note that I get heads and stop. If I get tails, I then roll the dice. If the dice roll results in a 4 or higher, I note the result and stop. If dice roll results in a 3 or less, I start over with the coin and repeat until eventually reaching a terminal state (either a head on the coin or a 4 or higher from the dice)
What I'd like to know is how to analytically determine the probability of each the terminal states for any given attempt, assuming that you always go until you reach a terminal state.
The recursion is really throwing me for a loop, I'm not even sure what the proper term for a situation such as this is.