The birthday problem/paradox
The birthday problem (or birthday paradox) refers to the probability that, in a group of N people, there is at least one pair of people having the same birthday. Surprisingly, you need just 23 people to have more than 50% chances to find at least a pair! Yes, only 23! Not, as you could think, 183! There are a short and a long versions of this post. The short one ( aka what you have to remember to impress your friends ) is: In a room with 23 people there are more than 50% chances (50.73% to be precise) to have a at least a couple sharing their birthday. With 50 people, the probability is 97.04 % and with 80 people we arrive to 99.99% changes to find such a couple! How is that possible? The rest of the post (the long version) proves the previous numbers. First of all, we have to make some basic assumptions: We have no twins in the room. No one is born on February, 29th! (we do not consider leap years) Every day is as good as all the others. In probability, the th