The birthday paradox
Yesteday I learnt about the birthday paradox. It's a counter intuitive event that shows why humans are not able to understand exponential curves. Our brains are wired to think in linear regressions.
Let's go straight to the paradox.
There is a room with 23 people. What is the probability of 2 people having the same birthday?
One would think that it's unlikely that in a room with 23 people 2 will be born int he same day.
The probability is 50%!!
What the hell, how is that possible?
Learning more about the birthday paradox
After getting shocked with this information I started doing a quick google research. Something must be wrong here.
The key factor here is that our mind tries to solve the problem by comparing 1 persons birthday to the remaining 22, and it forgot that this calculation needs to be done again for the rest of the individuals. Which adds more chances to match.
This result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals. With 23 individuals, there are 253 pairs to consider, far more than half the number of days in a year.
Here you can also find the probabilities from the wikipedia site:
With 60 people you have a +99% chance of coincidence
Amazing that with just 60 people you would probably have 2 with the same birthday date.
In fact, it shocked me because when I was in school I had the same birthday as a friend.
We both thought this was extremely difficult to happen, but in fact, it is not.
Math never lie!
The lesson here is that our brains are not prepared to think in exponential terms.
Thats why compounding interest is the 8th wonder of the world!
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