Birthday Problem

Suppose we have 30 students in a class, what is the probability that at least two students have the same birthday, i.e.,

This problem is easy to solve:

As shown, the probability is pretty high.

Another expression of birthday problem is like this: How big the class is to make sure there is >50% chance that two students have the same birthday? Namely,

We can solve the above equation, and n is approximately 23, i.e., if the class has 23 students, there is >50% chance that two students have the same birthday.