I'm having two binomial cdf cases and I'm looking for the minimum number of samples to satisfy each one:
- p = 0.1 and we want 90% probability to have 5 or more successes.
- p = 0.3 and we want 90% probability to have 15 or more successes.
Intuitively it looks like the answer would be the same in both cases since p was tripled but k was as well. However I do understand the logic behind the difference in the amount of samples needed, but can't really prove it well or generalize it. What is the mathematical reason for this difference?