If there's an event that has $N$ chance to occur, what is the probability that over the span of $M$ attempts it will happen exactly M*N times?
Example: $0.1$ chance to get $A$, $0.9$ to get $B$. What is the probability that over $10$ repeats it will be one $A$ and nine $B$'s? And over $100$ repeats to be $10:90$? Intuition says that it should be (1-chance)^times but then the chance is the lower the more repeats there are. However, in real life, the more repeats, the more the ratio approaches probability ratio.