We have covered conditional probabilities and law of total expectation so far but I have a very poor understanding of those concepts. I have absolutely no clue on how to proceed with this question:
A fair die is thrown and a coin is tossed the number of times as the score shown on the die. If any heads are shown in the tosses of the coin, we stop, otherwise, we continue the experiment of throwing the die and coin toss until at least one head is shown. Find the expected number of coin tosses before we stop.