# Probability of birthday in a group of N people

What is the probability that on any chosen given day (e.g. today) there is at least one person (in a group of N) who is celebrating his birthday?

I would say the answer is either $N/365$ because you get $\frac{1}{365}+\frac{1}{365}$..$N$ times or $1-(\frac{364}{365})^N$ because this is $1$ - the chances of all N people having birthday on a different day other than the chosen one.

Which is the right one(if any is) and why?

The last one i.e $1-(\frac{364}{365})^N$ is the correct answer[Here $\frac{364}{365})^N$ is the probability that $N$ people has birthday in all the days except your specified day & you take the complement of that event, which is needed.] . Because your 1st answer implies choosing $N$ days among $365$ days in a year. Does satisfy your requirment.