# The Birthday Problem

If you keep tabs on birthday notifications on Facebook, you’d realize some of your friends do share a birthday. If so, what are the chances of two randomly chosen friends having the same birthday? This is a well-studied problem in statistics referred to as the ‘Birthday Problem’, which states – If N people are in a room, what is the probability of two people sharing a birthday? I decided to investigate. Straight to my Facebook account, I collected 628 friends’ birthdays, wrote a script and bingo I had a graph.

A shown on the graph above, there is a 0.5 probability of sharing a birthday in a group on 24 people and a 1.0 probability in a group of 70. The interesting bit of this problem is the fact that most people expect a group larger than 365 people to have a chance of sharing a birthday. Go to Facebook  >  select 70 random friends  >  you’ll be guaranteed at least two of them share a birthday. This is not just fancy recreational mathematics, a lot of computing, engineering and scientific processes rely on this concept.

In medicine, the concept is used to calculate  Class Phenotype Probability – the chance of two people sharing the same blood-type? This particularly important in calculating the likelihood of finding matches between donors and recipients in blood transfusion. In cryptanalysis, a code-breaking technique known as the birthday attack utilizes the same concept to find chances of a pattern repeating itself in an encryption scheme.

Since the US has had 44 presidents, according to my graph there’re 0.89 chances two of them will share a birthday. Bingo! Yes! Warren Harding (29th presidents) and James K. Polk (11th president) both have a birthday on November 2nd.