My Brain- AWGN!

Earlier this week, I made a funny observation. I get really pissed off if my pen runs out of ink when I'm writing something important. That's one of the reasons why I lived on other people's stationery for major part of my under grad life (some self consoling justification for my frugal existence !!). In an attempt to turn a new leaf, I decided to do this- I put 3 pens in my bag and every morning, I would pick one at random and use them. I thought all the three pens cannot obviously run out of ink the very same day. On Tuesday during my Linear Systems class, the pen I was using went dry. Then I took another one from my bag to find the same response. Holding my breath, I took the last one out and to my shock, even that ran out of ink!!!

After the class (of course, I borrowed one from my neighbour for the rest of the class as usual!) as I was going back to my office, I was trying to figure out if this was sheer bad luck or if there is an explanation for this. And I found that ideally, according to the way I was using the pens, the probability of all the three pens running out of ink the same day is one !!! To put it in simple terms, lets assume each pen has enough ink to last for 30 days. So no matter how I use them, I cannot use all of them put together for more than 90 days. So, if my selection of pens everyday is completely random (that is every pen has equal chance of being chosen each day), then on the 90th day(assuming 90 is a fairly huge number for statistical purpose), I would have already used each pen for about 30 days. And hence they would ditch me together.
Moral of the story-
1. I'm capable of creating ideal noise in my decisions!
2. Miserliness is a virtue that never fails!