help with conditional expectation

if we have a crooked coin, with P(H)=0.55 and P(T)=0.45. Then what is the difference between finding E(X) and E(Y) . Given X is the number of coin tosses until 2 successive heads (HH) occur and Y is the number of coin tosses until a head is immediately followed by a tail (HT)
does a crooked coin effect the method of finding E(Y) different from finding E(X) due to the chance of getting heads is more likely than getting tails ?