Brainwashed by statistics

Whenever I go home from work I hope to run into a certain friend of mine. He usually takes the same metro as I do. Depending on the traffic he either takes the front entrance or the backward one.  What happens to me every single time I try to find him? My (obviously damaged) brain calculates, that the average of his presence is right in the middle of the platform. So I wait there. Although I do know (given, that his |Ψ(x)|²  → 1 to be found at the front entrance at heavy-traffic-days and analogue for the backward one at not-so-heavy-traffic days) his
|Ψ(x)|² to be found at the middle of the platform aims 0. Stupid, huh? 

These are the days when I can't stop wondering, why humans act against their nature. If we'd just respect the laws of physics, wouldn't be life so much easier? Wouldn't it just be wonderful? Actually it's a bit like traffic accidents. If every single driver would respect the rules, there were no accidents. Why do we human beeings think we are "smarter" than the universe? Gosh, why can't I be a photon? I would fly arround and make jokes of people, who belive to know everything. And: I'd find my "Mr.-Right-Photon" more easy ;-)