Hello, given graph $G=(V,E)$ with $n=|V|$ and $k=|E|$, what is the probability that it does not contain any cycle $C_l$ for $l\geq3?$
The requested clarification: My intention was to form the question in such a way, that there is no information about any distribution of the edges, and n and k are parameters. This lack of information should be in fact the information. You construct graphs in any possible ways, and you have to decide which constructs are more possible to occur and which are less expected. This probably implies the uniform distribution.