I was in a Mathematics Museum today and I came across the following interesting table. The table was a large circle that had a few parallel chords passing through it. It looked like this but with more parallel chords until the end :
There were also 22 small circular discs. The board beside the table said to throw the 22 discs randomly on the table. Once you are done, count the number of discs (from the 22) that intersect with any line, and call that number $x$. The calculate the value $22/x$. Repeat this process 3 times and take the average. When I did this, the average was extremely close to $\pi$! (Just like the board said it)
I couldn't help but wonder why this happens? I am thinking of throwing 22 discs as bernouli trials and we want somehow that the Expected number of discs intersecting the lines to be 7 (so that this works). However, how do you calculate the probability in this case? (i.e. the probability of success)?