Understanding the Birthday Paradox
How many people do you think it takes in a room for two of them to have more than a 50% chance of sharing the same birthday? Surprisingly, the answer is just 23 people!
The birthday paradox is a fascinating observation of the average person’s ability to estimate probability. This sheds light on human behavior and the tendency to be impacted by subconscious bias when estimating probabilities. The quiz above and the calculator below provide further evidence, illustrating that it only takes an average of 23 other individuals in a room to have a 50.7% chance of sharing a birthday 1. With the awe-factor aside, there are several design-oriented lessons to be learned from the paradox.
Move the slider below to see how the probability of shared birthday’s increases with the number of people in a room.
What does this have to do with design?
This post is an attempt to delve into the relationship between people and their ability to calculate probabilities ad hoc. Personally, I tend to overinflate my understanding of what is going to happen in the future. With this awareness, I think I’m supposed to temper my judgements?
This post was inspired by Daniel Kahneman’s book, Thinking Fast and Slow. In this book two distinct systems of thinking are outlined. The first system is characterized by rapid, autonomous responses that are reflections of an impulsive understanding of our current situation. System 1 can be seen in action when driving on a highway, for instance. Imagine the person in front of you slams on their brakes on the highway, coming to a complete stop. Your response to such an event (braking hard, switching lanes,… etc.) is an instance where system 1 is in control. System 2 is responsible for deliberate focus and mental efforts. System 2 is employed in complex calculations where sustained attention is required to ensure the accuracy of the results — maybe your taxes for instance.
System 1 detects simple relations and excels at integrating information about one thing, but it does not deal with multiple distinct topics at once, nor is it adept at using purely statistical information. (Thinking fast and slow, pg 36). With that being said, spontaneous probability calculations fall in system 1’s domain. The logical error in the birthday paradox occurs because system 1 specializes in focusing on one factor at a time, not multiple factors. Many who attempt to answer the birthday paradox compare themselves (one factor) to everyone else. The thinking generally comes up with a statement similar to “how many people in this room share a birthday with me”. This is likely a subconscious thought in the process of the calculation (which is typical of system 1 processes). However, the true question should focus on the connections between each person in the room. These simple diagrams illustrate how it is possible to have much greater odds of a shared birthday between two people in a relatively small group.
Framing the problem correctly is the most important aspect of leveraging past experience to our current situation.