The Monty Hall is quite an interesting puzzle from the 1970’s. The problem goes as such, you have 3 doors, behind one of them is a car or something worth value. Behind the other 2 doors is nothing worth value. You can pick a door and whatever is behind it will be yours. After you pick a door however, the host reveals one of the doors that has nothing in it and makes you an offer to switch doors, or stick with your original choice. Most people would stick with their guts and stay with their original choice, however this is a huge mistake. To put it mathematically, when you first choose your door, you have a 33% chance of getting the lucky one. However, when he reveals one of the doors, your odds actually go up to about 66%. Some people wrongly assume that you have a 50% chance when this change happens. If I were to tell you to pick a single card from a deck of cards, it would have a 1/52 chance that it was the ace of spades. If I then were to turn over all cards except 1, and the cards turned over were not the ace of spades, the left card would have a 51/52 chance of being the ace of spades.

Now and again an average worker will come up with his own idea on how to revolutionize his company. Unfortunately, most companies aren’t looking to be revolutionized. Many bosses practice the idea of killing off good ideas. If your company is doing well and making money, what’s the point of change? I’ve heard a saying from my dad that said, “If something works, don’t try and fix it” This may seem odd but it is present to most of us. I can’t tell you how many times I’ve mentioned to my mother that her check engine light was on, or that the vehicle said maintenance required, and she shut me down because the car worked perfectly fine right now. These are machines that have killed people before and I am being told that since the car still moves, we shouldn’t be worried that something might be broken. Killing off good ideas can be a counter intuitive way to keep a business functioning and even though it seems kind of sad, it works.

In times of war, aircraft are a looming threat that can’t be left alone and need to be dealt with. Unfortunately, since small arms fire does not have the required range to eliminate an enemy air threat, we need to use special weaponry called anti-aircraft. In order for planes to be more effective against areas with anti-aircraft guns, we decided to put armor on the planes to make them more resilient. Where we put the armor though is the interesting part. After observing planes that have returned from the battlefield, we could see where the planes were hit. You might think that if we put armor on those spots, they would be better on the battlefield but you’d be wrong. You have to remember that these are planes that have returned from the battlefield. These planes have been shot and have returned. So statistical reasoning deduces that we put armor on the plane where it has not been shot. This might be a counter intuitive way to deal with a problem, but it works just as much.