It looks to me like you want from Theorem 1 in this paper.
This was found by googling Bernoulli trials success runs.
Hi guys, first time poster. I hope this section is the most appropriate for my problem - please feel free to move it if it is too basic
A fair coin is flipped n times.
What is the probability that there are at least k consecutive heads in these flips?
If the k-generalisation is making the working awkward then please just solve it for k = 2 because I think I know how to get from there to the general answer.
Thanks for any help you can give me!
It looks to me like you want from Theorem 1 in this paper.
This was found by googling Bernoulli trials success runs.