Why does this work when M=34 but not when M=35?:
Clear [n, M, confidence, k, p]; n = 8; M = 34; confidence = 0.5;
$ \text{Solve}\left[\sum _{k=n+1}^M \frac{M! p^k (1-p)^{M-k}}{(M-k)! k!}=\text{confidence},p,\mathbb{R}\right] $
Thanks!!
This code works on my system:
With[{M = 35, n = 8, c = 1/2}, Solve[Sum[(M! p^k (1 - p^(M - k)))/((M - k)! k!), {k, n + 1, M}] == c, p, Reals]]
