The question is from a Master-level Probability Course.
It is well known that the underlying assumption for the binomial distribution is that there are n independent Bernoulli trials. More specifically, the assumptions are:
(1) The number of trials, $n$, is fixed.
(2) There are two and only two outcomes, labelled as "success" and "failure". The probability of outcome "success" is the same across the n trials.
(3) The trials are independent. That is, the outcome of one trial doesn't affect that of the others.
My question is, are there any counterexamples which just violate one of those three assumptions? Particularly, are there cases where Assumption (2) holds but (3) doesn't, or vice versa?