I recently came across this this thing called the birthday paradox. It asks for probability that at least two people in the room of n randomly chosen people, will share the same birthday. Surprisingly according to its theory, only 23 people are needed to have 50% chance for two of them sharing a same birthday and 72 people to have 99.9% chance. It seems counter intuitive at first but it is in fact, real. There is real math to prove it (Probability and simple permutation and combination).
The website is not yet complete. I have just completed the basic calculation part and plotting the probability graph (Total time spent in making: 45 mins). There is still lot more work left (mainly layout and designing plus adding some more content). I do not plan to complete the work anytime soon because of time limitations.
It is a fun project. You can play around for a while.
I will leave some links about this problem
Birthday Problem - Wikipedia
The Birthday Paradox - YouTube Vsauce2
Check your intuition: The birthday problem - YouTube TED-Ed
Birthday Problem - Brilliant Math & Science Wiki