# Real World Probability: A “Birthday Problem” Anecdote

I heard the following story from my topology professor.

A renowned statistician was teaching a course in fundamental probability theory to a group of undergraduates. As expected of an introductory course, he briefly tackled several main principles of probability to give the students a bird’s-eye view of the subject.

One day, he talked about the famous “Birthday Problem”, which states that a room with 23 people is enough to make the probability of two people sharing the same birthday higher than 50 percent (the exact probability is 50.7297 percent) and it would only require 70 people for the probability to become 99.9 percent.

“This is a rather sizable class. So, the odds of two people having the same birthday in this room is huge!” the professor said confidently.

The professor was bemused when the class suddenly burst out laughing. It took some time before their laughter stopped, and he still couldn’t figure out what was funny. Unknown to him at the time, there were two identical twins sitting next to each other in the front row.

### Posted by Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

## 11 thoughts on “Real World Probability: A “Birthday Problem” Anecdote”

1. Make me think. This is an interesting dynamic. I always look for the group that will provide any aspect of bond or tie. There can always be something that could bind perfect stranger. Very interesting.

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2. Ha ha, I wonder if there were other people with the same birthday in that classroom.

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3. The probability that there will be at least two students in any class who will attempt to make a fool of the teacher is about 98.9859% or something approximating that.

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4. My father was an instructor for the Navy. At the beginning of each semester, he’d make a bet with one of the students that two of them had the same birthday in the class room. He won most of the time and afterwards, would explain it to them.
BTW, I’ll read any post that starts with “I heard the following story from my topology professor”

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1. Of course, it is probable that identical twins could be born on different days. Especially if the first is born at 11:59PM!

Loved the post though…

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1. It would be more fun if this happened in different time zones. For example, the first twin was born on Jan. 1, 2019 at 12:00 AM while the younger one was born on Dec. 31, 2018 at 11:35 PM.

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2. Some Stats course students in my university would also do a similar thing and fooling their friends in other programs. They would enter a lecture hall which usually have 80 to 100 students and make the bet. Since there are 365/366 days a year, the other parties felt that the odds favored them.

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