Wednesday, April 23, 2008

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.

6 comments:

Lara said...

I blame the following comment on my lowered brain power due to a cold and much cold medication.

heh. funny.

erin said...

Eric, you should See Please Here.
Apparently this will solve ALL your problems.
Nice visual aids, btw.

erin
blog: jewellerybyerin.blogspot.com
d-aunting-prospects.blogspot.com

Lida said...

You can always blame it on Mom. Somehow that works for a lot of things.

Enchante said...

Probability is a funny thing. I am assuming that each time the clip moves one way or the other that the probability of it falling off is dependant on that swimg, it will be smaller or greater (depending on which way the clip moves).

The 1 in 18 or 1 in 12 maths ia a bit off, because you have to subtract the degrees in which it might not fall off.

You also have to calculate the how much time you spend the day walking, how many times a day you get up and sit down. When are the times your keys for off etc etc.

To get the most accurate information, you will probably need to a regression test.

Sound complicated?

anyways, on a lighter note, still loving the blog and am going to add you to my blogroll!

Enchante
myphilosophicaldiary.blogspot.com

(slightly) less cynical said...

I forgot about the degrees it may not fall off, which is similar to the calculations of Expected Value in poker books... then again I start glossing over the sections when formulae start appearing...

The probabilities I encountered while tutoring grade 9 students involved pulling marbles out of bags... and when I took Statistical Analysis the teacher said "Let's just stick to coin flipping and dice, because a deck of cards is too complicated."

Enchante said...

Yeah, well most probability in schools is very one dimensional and most of it is independent (flipping a coin or rolling a dice). On the odd occasion there is dependent ones like pulling a marble out (only if you don't replace the marble).

The problem when you get to things like how likely my keys will fall off my key chain throws everything into the air because there are many many more variables, some are not important and some very. Which is why following poker probabilities isn't the best idea because a deck of cards only has one variable influence, which is what cards just hit the flop or turn.