A fun paradox I read about a few days ago that really caught my mind is the Inspection Paradox.
I tell you that a bus comes roughly every ten minutes. It’d be easy and logical to draw the conclusion that if you went down at any random time, you could expect to wait an average of 5 minutes for a bus. It always takes longer.
The problem with the above scenario is that since the bus comes roughly every ten minutes, there are times when the bus takes longer than that, and times when it takes less time. When you go down at a random time, you are more likely to end up going down during one of the >10 minute periods (because there is more time to land in).