I Tested the Birthday Paradox on People Born Between 1994 - 2014

Описание: The Birthday Problem is one of the most famous paradoxes in probability theory! How many people do you need in a room to have a greater than 50% chance that at least two of them share a birthday? The answer is much smaller than you think!

We solve this problem using three methods, from theoretical math to millions of simulations with real birth data!

What You'll Learn in this Probability Deep Dive:

The Problem: We define the core concept: finding the minimum number (n) of people required for the probability of a shared birthday to exceed 0.5 (50%). (Excluding leap year babies).

Monte Carlo Simulation (Initial): We use random sampling to quickly estimate the solution, demonstrating how Monte Carlo provides an accurate answer without complex math.

The Theoretical Solution: We simplify the calculation using the complement rule (P(shared)=1−P(no shared)) to derive the exact mathematical answer.

Real-World Data Test: We use 20 years of real birth data (from FiveThirtyEight) to create a sophisticated probability distribution and run 1 million simulations to see if real-world variation affects the "magic number."

Teachers and Professors: Sample your own classroom to test the results and post your findings in the comments!

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Want to learn more about experiments applied to mathematics, physics and engineering? Check out the other investigations we've looked at here:
   • Cody’s Science Experiments  
   • Investigating Myths with Math and Science  
   • High School & College Science Experiments  

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Chapters:
0:00 Introduction to the birthday problem and probability
1:30 Experimental setup
2:42 Our hypothesis about the total people required
3:09 Initial monte carlo results
3:28 The theoretical solution
4:15 A look at real data over 20 years
5:04 Final results with real data vs the theoretical solution
6:06 Bloopers
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Thanks to the news website FiveThirtyEight (‪@ABCNews‬) for making the data public.

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