# There are two students born exactly in one day of year. How to prove? [duplicate]

I remember once in our Statistics class, our professor mentioned an interesting problem, that is:

In our class, consisting of 30 students, I bet that there are two students born on an exact day of year.

It was quite clear to all of us that he will lose the bet, but then he asked all the students to write out their birth date on the board and surprisingly three of us were born in the same day of year!

It was very interesting to us. He wrote the proof to his statement, showing that If there are 40 students in one classroom, the probability that at least two students are born in the same day of year is over 90 percent (as I recall).

A few days ago, I told my friends about this, they all laughed at me saying it is impossible. I tried to give them the proof but I failed. I've forgotten everything!

I guess it is a famous problem in statistics, can anyone provide the proof or any link to any docs providing the proof to this statement?

• It think you are referring to the Birthday problem/paradox. – COOLSerdash Jul 15 '13 at 13:04
• That's it, thanks. If it was an answer I would accept it ;-). – Moh Jul 15 '13 at 13:14
• Thanks MOLi, I appreciate it, but my short comment does not qualify as full answer in my view. – COOLSerdash Jul 15 '13 at 13:17
• By the way, thanks again. I just called my friend and made him shameful of his laughter to me ;-). – Moh Jul 15 '13 at 13:19
• BTW: The number of students that you need, so that the probability that at least three were born on the exact same day is >0.5 is 88. For at least four, the number is 187. See this table. – COOLSerdash Jul 15 '13 at 13:30