I have a somewhat of a unique problem, I am trying to determine the odds of the following,
A Bernoulli Sequence where it follows the pattern of: Tails, Tails, Tails, Tails, Heads, Tails, Tails, Tails, Heads, Tails, Tails, Tails, Heads, ..., ...
I want to find the probability of each position occurring in this sequence, I started with the Binomial Distribution, but realized that utilizing this actually gives me the probability of the number of heads anywhere within the sample; with this in mind I changed to doing the normal multiplication method of (0.5)^n.
This would work normally except, for each small segment of tails there can be an infinite amount before a head appears. So for example this could also be a valid sequence: Tails, Tails, Tails, Tails, Heads, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Heads, ...
There needs to be at least three conesecutive tails in each tails section, but can go to an infinite amount. Any help with this would be appreciated. For the moment I am just working on the model of odds are <=(0.5)^n, n being the position in the series.