A coin is tossed until five consecutive heads appear. Model this process as a Markov chain where the states are the numbers of consecutive heads. (0,1,...,5).
a. Find the probability that it takes 10 or fewer tosses to observe five consecutive heads.
b. Find the mean number of tosses it takes to obtain five consecutive heads.
What I know - the probability of getting 5 H in a row is 1/32
I also know I shouldn't be confused about this, but I'm missing something.
Can you help?