The Birthday Paradox

By Anthony Gold

When I was in 9th grade, my statistics teacher performed an experiment in class that blew me away – and forever cemented my love of probability.

On the first day of class, this is what she said.

“There is greater than 80% chance that two of you in this room have the same birthday.”

I looked about the room and counted 35 students and thought, “No way!”

Here was my thinking: there are 365 days in the year. To guarantee that two people have the same birthday, there would need to be 366 people in this room. And while she didn’t say “guarantee”, she did say “greater than 80% chance”, and those are pretty high odds.

So, the teacher started down the line asking the first student to state her birthday. The teacher asked if anyone else had the same birthday. No one did. Now the second student stated his birthday. Again, no match. Third student stated her birthday – and I couldn’t believe it – there was a match in the room.

But once I did the math, I realized the teacher was right. It only takes 23 people in a room to have a greater than 50% chance that two of them will have the same birthday. Twenty-three! With 35 people in the room, it is 81% odds. And with 46 people in the room, there is a 95% chance that two people will have the same birthday!

While the math is fairly simple, the conclusion is mind-blowing. It completely defies common sense – yet the results are staggeringly true.

By the time I got to college, I discovered that nearly every math professor teaches the “birthday paradox” as a way to indoctrinate students into the realm of probability and the practice of not trusting our senses when it comes to distinguishing reality.

So what is reality?

Perception selects, and makes the world you see. It literally picks out as the mind directs. Perception is a choice and not a fact, [and is not] a witness to reality. (T-21.V.1)

The world you see is an illusion. (C-4.1)

Projection makes perception. The world you see is what you gave it, nothing more than that. (

Our [ego] senses tell us a completely different story – that this is real, and I am capable of suffering grief and sadness; or, conversely, that I can find joy and happiness in the world. But are our experiences and senses right? Not if they were made for the purpose of showing us what is not there. Join us in Monday’s class where we’ll explore this concept of sense-deception and how we can learn to see true reality and the associated bliss that comes from choosing such a state. And we’ll see who has the same birthday. I look forward to seeing you then.

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