Yes.

A bad recommendation can ruin your chances. If a letter writer were to write that you had committed some grave academic dishonesty, for example, that would look extremely bad for you, even if the others were generally positive.

An answer to another question says that even a "good but not great" letter could keep you out of some departments.

Can a single bad letter of recommendation ruin my chances of getting admitted to grad school?
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 ? 
