A company takes on an average of $0.1$ new employees per week. Assume that the actual number of employees taken on in a given week has a Poisson distribution.
Let $Y$ denote the number of weeks that pass without a new employee being taken on. Calculate the expectation of $Y$. Calculate the probability that, over the course of a year ($50$ working weeks), there is just one week when more than one new employee is taken on.