So I'm interested in the probability that an event will occur a set number of times in a larger number of trials, when the odds of that event occurring are known. Here's an example, let's say that the odds of me pressing a random key on my keyboard and that key being a number or letter is 36/108, so 1/3. My question then is what is the probability of a number or letter being pressed an arbitrary number or times in a arbitrary number of attempts. As in, what are the odds that I press a number or letter eight times in thirteen attempts. I would assume the answer would be that it is not likely for this to occur, given that the theoretical probability suggests that a number or letter should be selected only four times in thirteen attempts, given 1/3 odds, but I want to know the exact probability. Up until know I've been able to determine probability of situations like, "What are the odds that the colour green is never chosen on a spinner in nine spins, when there is 1/5 odds for green to be chosen". I would solve this by simply saying P of no green being chosen in 9 attempts = (0.8 ^ 9) \* 100 (percentage). Anyway, that is a really restrictive way of looking at probability and it doesn't work with the problem described earlier or anything more complex than that, so I would greatly appreciate some help with this. Thank you to anyone who responds in advance!