Does anyone remember the scene in 21 where Professor Keven Spacey is asking the protagonist about choosing behind three doors, two with a goat and one with a door behind it? Well in case you don’t…
3 years. 3 years ago I saw this movie on an airplane. 3 years later in a stats class I now finally understand this problem. I’ve thought about this problem many times over the 3 years and now finally. I feel so enlightened. That feeling of goodness at school would be second place right behind the last day of exams last semester. The sad part is that if I had wanted to know the answer enough, there are great explanations for how it works on YouTube.
The strangest thing that I can’t get over is that even though I know the answer, and cannot deny the proof that my professor showed us on the overhead, my head still makes it feel like it must be a 50-50 chance. It just feels natural that way. You’re a strange one, brain.
In case you were curious, the most easy to understand explanation that I came across was that when you first choose a door you have a 1/3 chance winning a car. So, the chances that the host has the door with the car is 2/3 since he has two doors. The fact that he shows you what’s behind one door doesn’t change the fact that his chances are still 2/3 while yours is 1/3. So switch.
For another taste of stats, or COMM 291, I’ll describe another exercise the prof gave us.
He holds up 3 slips of paper. The first one, pink on both sides. The second, green on both sides. The third, green on one side pink on the other. The professor hides them behind his back and then asks the class what is the probability that if he randomly chooses one that it will be the double green. The class is silent. We all think it is a trick and no one wants to make a fool of themselves. He reassures us that is it not a trick, although he also reassures us that half of the things he says are tricks. A student says 1/3. Correct. Now he picks a card and shows us one side. A green side. He now asks us what is the probability of the other side being green as well.
Care to take a shot at it?