# Sample space probability

Assume that the probability that a person is born on any given day is $$\dfrac{1}{365}$$ (ignoring February $$29$$). In a group of $$100$$, what is the expected number of sets of two people that have the same birthday? What is the sample space?

I am a bit confused for that question, any thoughts? thanks!

Let $$B$$ be a discrete uniform random variable, with values in $$[1,2,3,\ldots,365]$$. Each person's birthday is then one of these.
You have a group of $$n$$ people, and hence $$n$$ independent birthdays $$B_1, B_2, \ldots, B_{100}$$. How many pairs $$(i,j)$$ can you find that $$B_i=B_j$$?