Assume a fair coin is tossed $n$ times. I am looking for the probability that the sequence starts with an even number of consecutive heads followed by a tail outcome? I assuming that this means something along lines of summing over binomial distributions, but not really sure here -any specific ideas?
For example in the case of $n=3$: $$ TTT,HTT,THT,HHT$$ Then the following outcome fulfill the requirements: $TTT, HHT$