Consider $\mu_n$ an approximation to the identity; e.g. $$\mu_n = \frac n 2 \chi_{[-1/n, 1/n]} \lambda$$ for $\lambda$ the Lebesgue measure. Then $\int f\ d\mu_n \to \int f\ d\delta = f(0)$ for all continuous $f$; but $\mu_n({0})=0\to0\ne1=\delta({0})$.

uniformly continuous functions and measures
In the wikipedia page (http://en.wikipedia.org/wiki/Birthday_problem) on birthday paradox the following statement has been said : "the probability that, in a set of $n$ "randomly chosen" people, some pair of them will have the same birthday. We assume that that each day of the year is equally probable for a birthday."

My question is what is the meaning of "randomly chosen" here ? Is the assumption of equally probable for a birthday needed separately ? Does not the word "randomly chosen" imply the equal probability ? 
