The first task of today was if numbers were chosen at random, what would be the probability that numbers started with the digits 1 to 9. Of course the probability would be the same for each digit.
Ok, let’s see if this works. Go ahead and find any article, it can be a news article, a scientific article, etc. Now count the number of times that each digit 1 to 9 is at the start of a number. Does the distribution seem even?
Let’s see if this trend can be found in mathematical sequences too. Here’s an example: the Fibonacci sequence.
1,1,2,3,5,8, …
Let’s find the probability of numbers starting with digits 1 to 9 in the first 10,000 numbers of this sequence.
Quick tip: you can use excel to do this and then use the countif function to find the distribution of probabilities of numbers that start with each digit. Does the distribution seem even?
This strange pattern of occurrence is called Benford’s law, and it is very counter-intuitive.
If you would like to learn more, click on this link: https://brilliant.org/wiki/benfords-law/
So here is your final challenge: every single time you see a number today, write it down and you can then verify the law for yourself. How close did you get?