Probabilities

I have the tendency to leave keys behind when I lock doors, which is why it is important that my home can only be locked from the outside using the key. Not so for my office door - the day after getting my keys from security I managed to lock myself out of my office. I was informed that it was a rite of passage as I was handed a duplicate key by the receptionist. A coworker pointed out that she kept her keys on her lanyard with her ID, which I thought was a great idea.



Of course, having your keys a foot below your chin is kind of annoying when you need to unlock your door and you're too lazy to remove the lanyard from around your neck. Soon I began to feel a bit silly kowtowing to my doorknob several times a day.

Now, when I worked as a co-op student in the government, our IDs were on round belt clips which extended like a spring-action yoyo. I still had the belt clip, so I clipped my ID to the extending clip, and attached that to the lanyard.

Here's where I get into the probabilities of things. It's been a while since I tutored grade 9 mathematics, but here's how I calculated it:

The flat belt clip hangs in the loop of the lanyard, with only a small hole for it to enter and exit. The belt clip can exit straight out of the small hole only from certain angles. I estimate it to be a range of about 20 degrees, able to exit only from one direction.


In addition to this, there's about a 30 degree range at which the clip can be pulled through the hole with the ring rotating around the clip.


So that's a one in eighteen chance of the clip being able to exit at a single degree of rotation, and that rotation has a one in twelve chance of being lined up as well. To have both of these angles line up exactly aimed out the small gap, there's a one in two hundred sixteen (1:216) chance that the clip will be able to escape from its circular prison.

So why is it that when I'm wearing the lanyard while walking into the office, or sitting down at my chair, or leaning forward ever so slightly, or standing perfectly still while a butterfly flaps its wings in Auckland, that my keys and ID will crash to the floor, two or three times a day? My probability calculations don't even include the chances that my body will move in such a way that the clip will, once lined up, be propelled through the tiny little hole in the loop.

It's obviously a similar to the law of chaos which oversees how earphone cables tangle into knots when left alone on a flat surface.