# The Birthday Problem

I’ve heard of this ‘problem’ numerous times before, as I’m sure many others have too. Nonetheless, everytime I do hear it, it fascinates me.

The birthday problem (or paradox, as it’s often referred), looks at the probability of two or more people from a randomly chosen set of people sharing a birthday.

In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will both have been born on the same day. For 57 or more people, the probability is more than 99%, and it reaches 100% when the number of people reaches 367[â€¦]. The mathematics behind this problem leads to a well-known cryptographic attack called the birthday attack.

## 2 thoughts on “The Birthday Problem”

1. Libby

I had a psychology prof, who, in 20 years of teaching classes of 30-35 people never had a class without 2 students with the same birthday. Go figure.

2. Lloyd Morgan Post author

Thanks for the comment and the interesting anecdote, Libby. Here are some further probabilities in this context:

30 people in a class: 70.6%
35 people in a class: 81.4%