Chemical and Biomolecular Engineering

Official blog of the Lehigh University Chemical Engineers

Having the same Birthday Paradox?

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In today’s Unit Operations recitation, we stumble upon the famous mathematical problem: The Birthday Paradox.

Basically, we were discussing how the science of probability is very counter intuitive. The professor begins by asking what do we think the probability is that two students in the room have the same birthday. There was about 60 students in the class, so I thought it’s going to be something like 60/365, so pretty low. However, the question is very misleading. In fact, you reach 50% probability with just 23 people, and 99.9% with 70 people. In fact, he’s right. There’s two students who actually share the same birthday. The thing with probability is that it doesn’t always happen, but it’s likely to happen, and it works better when you have a very large random sample. Say you have 500 friends on facebook. It’s over 99.9% that you’ll have two friends share the same birthday, but on same days none of your friends share the same birthday, and on some days three of your friends have the same birthday.

Here’s a picture to demonstrate the probability increase over number of people.

 

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Author: Jerry Jin

Hello, My name is Jerry Jin. I'm a senior at Lehigh University pursuing a degree in Chemical Engineering. I'm from Allentown, PA, but I was born in Shanghai, China. I moved here when I was fourteen years old. I'm currently the secretary for Southeast Asia at Lehigh Club, and treasurer for SASE. I'm also on the Lehigh Ultimate Frisbee Team and I enjoy being spontaneous.

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