I recently thought of the following problem and my basic grasp of probability and combinatorics is not enough to handle it:
You flip a coin N times. What is the probability P(N,H) that you get at least one sequence of at least H heads in a row?
Since this question deals with the number of times a result will happen, I tried to use a Poisson Distribution, but I'm having trouble separating the problem into mutually exclusive events.
I wrote a program to do a simulation and found that P(20,7) ≈ 0.058, so please make sure your answer fits with this result.
Thank you for your help!
I tried this approach and got but kept getting answers that were roughly 2x too large.
I've realized that this approach counts certain answers twice. For example, for n=7 and h=3, the series HHHHHHH is counted 5 times, as RHHHH, HRHHH, HHRHH, HHHRH, and HHHHR. Do you have any tips on how to fix this?