Birthday Paradox

Paradox: A statement that seems senseless, even though it’s possible or true. Probability of having same date of birthday in a certain group of people, Suppose In a room of just 23 people there’s a 50–50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching. This is so called as Birthday Paradox.

Graph showing relationship between probability of two people having same birthday vs no. of peoples

The graph above clearly depicting that if there is a group of 23 people then the probability of two people having the same birthday is 0.5 that is equals to 50% chances of having a same pair of birthdays. and the graph becomes straight line means probability is equals to 1 that means 100%.

Here is a little demonstration of how it works, let’s have a look;

365 is the no of unique days in a year and 23 are the no. of peoples

But there is at least one excellent practical application using Birthday Paradox , i.e computer hacking. There is a Cryptographic computer attack known as the “birthday attack” which exploits the math of the birthday paradox. Using this method, a programmer can store the results of the birthday math in memory to decrease overall processing time when doing certain computationally useful things, such as attempting to crack a digital signature.