Maths Beats Intuition probably every damn time

Newton once said that “God does not play dice with the universe”. But actually he does. Everything happening around us could be explained in terms of probabilities. We repeatedly watch things around us happen due to chances, yet we never learn. We always get dumbfounded by the playfulness of nature.

One of such ways intuition plays with us is with the Birthday problem.

Problem Statement:

In a room full of N people, what is the probability that 2 or more people share the same birthday(Assumption: 365 days in year)?

By the pigeonhole principle , the probability reaches 100% when the number of people reaches 366 (since there are only 365 possible birthdays).

However, the paradox is that 99.9% probability is reached with just 70 people, and 50% probability is reached with just 23 people.

Mathematical Proof:

Sometimes a good strategy when trying to find out probability of an event is to look at the probability of the complement event.Here it is easier to find the probability of the complement eve…