If a city has an average of two accidents per day, how many accident-free days do you expect in a year?
Are we allowed to assume that the data come from a certain distribution? If yes, then this question can be answered. If no, then I can't think of a way to answer this question.
This data seems to come from a Poisson process, with a rate of lambda = 2. That is, accidents occur at a constant rate, accidents are independent and that there cannot be simultaneous accidents. The second and third assumptions are more questionable than the first, but I will just go with the Poisson assumption for now.
If lambda = 2, the probability that there are zero accidents in a given day is .135. The R code for this is $dpois(x=0,lambda=2)$. If we assume that there are 365 days in a year, the number of days without an accident is binomial with n = 365 and p = .135. Therefore, the expected number of days without an accident is 49.38.
The key step in this argument is to find the probability that there are zero accidents in one day.