I am having a problem with part c of a three part problem. The problem is as follows.
Independent flips of a coin that lands on heads with probability $p$ are made. What is the probability that the first four outcomes are
c) What is the probability that the pattern $T,H,H,H$ occurs before the pattern $H,H,H,H$?
Hint for part (c): How can the pattern $H,H,H,H$ occur first?
Solution for (a): Since these events are independent we have $P(HHHH)=pppp=p^4$.
Solution for (b): Likewise, $P(THHH)=(1-p)p^3$.
Thoughts/confusion for (c): I am confused what they mean by "before." I am also confused at what is mean by the question "how the pattern $H,H,H,H$ can come first" I mean it seems to me it can only come first if I do not flip a tails on my first flip, hence it would just be the same exact solution to (b), but I don't think it is asking the same question. If it is asking the same question I do not see how they are equivalent. Could someone help clarify please?