We’ve all had the experience—over and over all the time. You go down to the street to wait for the bus (the train, the subway, the boat); you know that buses come roughly every 10 minutes, so you expect to wait about 5 minutes (arriving, on average, in the middle of the between-buses interval). But in fact, we all know that almost always you have to wait longer than that! Is this an illusion we’ve developed over the centuries because we believe in the “persistence of bad luck,” or is it, perhaps, something real?
It is, in fact, a real phenomenon, and this result can even be proved mathematically. Because you arrived after the last bus has left, your overall waiting time is, on average, longer than half the average interval of 10 minutes.