Whacky Buggy Wheels

Okay, there are a number of strange and frequently periodic occurrences in my life that, over the years, I’ve come to simply accept. Everyone’s heard the saying about there never being a policeman around when you need one. In my case, true enough. But I’d like to expand upon this truism, in the case of my reality, to include bathrooms, a cold beer and girlfriends. However, I’ve grown to overcome most of these inconvenient inconveniencies for the sake of my own sanity.

In the case of policemen, well, first of all I try to avoid them. But there comes a time in everyone’s life when a policeman is needed. So, I also always carry my cell phone. There, problem solved. As for bathrooms, I can always find an out-of-the-way bush or back alley, disgusting but sometimes necessary. Beer? That’s easy; always know where the nearest convenience store is located. GPS works well for this and I strongly recommend purchasing a cell phone that has a GPS app. See? Two problems solved with one solution. And finally girlfriends, even easier, don’t have one, became a eunuch, that’s my solution and so far it’s worked well.

But, there’s one vexing occurrence in my life that I can’t seem to overcome; that of always selecting the shopping cart with the bumpy wheel. For some unexplainable reason, every single time I go to Wal-Mart, invariably I always pull a buggy from the buggy queue that has a wheel that is not sufficiently round. And, it doesn’t matter which Wal-Mart I go to, as there’s one every few blocks. Likewise, it doesn’t matter which queue I select, left, right, middle, middle left, middle right; the result is always the same.

I’ve come to realize that this is the great challenge in my life, the ultimate question, like seeking the answer to the big-bang, or why people think Keynesian economics will work in reality, even though it never has. But that’s another BLOG.

Now, I’ve studied this question from a probabilistic point of view. After all, it really is simply a question of probability. For example, if we know the number of buggies Wal-Mart has then we can easily determine the number of buggies with defective wheels. (Of course this is only applicable to a single instance of Wal-Mart as sample sizes and the normal distribution is beyond the scope of this diatribe, thank goodness.) We also know the number of buggy queues Wal-Mart has, five, and again with some sampling over time we can determine the average number of buggies that are queued at any given time. But, to keep it simple, let’s assume all the buggies are queued, we know the total number of buggies, we know the number of buggies with defective wheels, all queues are the same depth, and to make it even easier, each queue contains the same number of defective buggies and I'm the only person around. Then the probability of me selecting a defective buggy is simply:

P(that a defective buggy is in the front of a queue)*P(that I select that queue)

So, given all my assumptions, it’s pretty easy to figure out. If we plug some reasonable numbers (I assume) like total buggies equals 100, ten are defective, each queue is 20 buggies deep and I select the correct queue (1/5) we can conclude that the probability of me selecting a defective buggy is:

100/10 = 10% of the buggies are defective

100/5 = 20 buggies in each queue

20*10% = 2 defective buggies in each queue, then

P(that a defective buggy is at the front of the queue) = 2/20 = 10%, and

P(that I select that queue) = 1/5 = 20%

Therefore, the probability that I will pull a defective buggy is 2%, and that’s not even considering all the real world activities I’ve assumed away. 2% - I simply don’t get it.

In reality, the actual probability is probably closer to the same odds of being struck by lighting.

Anyway, I’ve come to accept this anomaly. It’s simply not worth the stress level. Yet, I continue to consider the mathematics as I embarrassingly smile and push my buggy through the overly-stocked Wal-Mart isles, ka-chunk, ka-chunk, ka-chunk. Now why couldn’t I have been cursed with this spell when it comes to the lotto? Of course I could always exchange buggies for one with four round wheels. Yes, that would make my life easier. Never mind….