The Birthday Paradox

I was interested to read about the birthday paradox in clay Shirky’s book entitled Here Comes Everyone: The power of organizing without organizations. I have limited exposure of this paradox, though I remember distinctly learning about the idea in my undergraduate statistic class. It was one of those class periods where the professor seemed so excited about the information and was sure that I and my fellow students would have a moment of clarity and understand. Unfortunately I did not remember even the name of the paradox… I only remembered to take the bet! I suppose that as a student I just played along as if I understood simply because I didn’t want to hurt the professor’s feelings. (I am sure my students do the same to me…pity nods and understanding facial expressions).

I was determined to figure out this problem as a tribute to my long forgotten stats professor. In doing so I came across the following website that made me feel smart for not understanding and then dumb for still not understanding. Perhaps you’ll have better luck: http://betterexplained.com/articles/understanding-the-birthday-paradox/

According to Cannon (personal communication, April 21, 2009), a local high school math teacher, the paradox states that when twenty or so people are in a room, there is about a 50% chance that two of them will have the same birthday. Our human brains works linearly and therefore this idea is hard to grasp. In order to solve the problem Cannon (2009) explains that most people think multiplication will help solve the problem, but really exponents are needed… Unfortunately my eyes glazed over here!

After another explanation from Cannon and rereading Shirky and Azad’s explanations, I am still lost. Here is what makes sense at this point. If I were to meet someone today walking down the street and ask him or her what his or her birthday is, the probability of us having the same birthday is extremely low. Likewise if I asked all the students in my class if they shared my birth date there is still a small chance that we would find a match. This changes when I ask each student to ask their peers if they share a birthday. Thus the number of people asking each other increases and thus the probability of finding a match increases significantly.

So what does this mean for me? 1) When carpooling with only one other person, my life is simple; I call Cheryl we set a time. When I carpool with three other people, the goal of setting a time becomes more complex. 2) I have something to blame my classes’ indecisiveness on. Let me explain…I would love to give students lots of freedom and give them complete control over certain aspects of class. However the amount of time it takes for the class to make a decision is astronomical!! In the process of making a decision (no matter how bid or small), I notice some students become annoyed with the organization and ask me to just make the decision. Sometimes I do make the decisions about class, but I still offer reasonable choice within any given topic.

Azad, K. (2009). Understanding the birthday paradox. Retrieved from Better Explained Web site: http://betterexplained.com/articles/understanding-the-birthday-paradox/

Shirky, C. (2008). Here comes everyone: the power of organizing without organizations. New York: Penguin Press.