In high school I recall my teacher explaining this paradox. She said theoretically if there were 23 students in our class, the probability of two or more students have the same birthday is 50 percent. So my question is, in a class everyone is born in the same year would this reduce the probablity?
[…] birthday paradox checks out. Pre was born not only on the same day as I am, but in the exact same year. And, since […]
I’m no mathematician but I am very intrigued by it . I have come up with a simple answer for this problem for thoughs who think in a way I do. I start off by assuming that there is on average 30 days in each month so imagine a calendar with 30 days so don’t imagine the specific days but when you think that each month has the same numbers it actually makes more since so instead of writing all the math think in normal ration terms. If you get 23 people in a room with the same birth number not month then you know you have about a 23 out of 30 chance not that’s pretty high well there’s only 12 months and thoughs chances slim down a bit but anyway that’s my quick thought on it
Hi, Kalid. I loved this post. Very interesting stuff!
I work with someone who was born on the same day in the same year in the same state only a few hours away (opposite coast from current residence) and only 2–3 hours apart. What are the chances?
@Kat: Whoa, that’s awesome you’re getting this so early, you’ve got quite a head start! More than welcome!
Thanks Kalid! That’s perfect.
Here’s what I came up with if anyone if interested. Just having some fun with numbers and the Olympics.
If I got something wrong, let me know.
@Nathan: The trick to remember is the paradox is about everyone else not getting overlaps either (i.e. Billy and Joey could have an overlap, and it would count).
@Kristina: Yep, with 30 people it starts to get pretty likely there’s be an overlap! Pretty amazing.
Hi
I need to calculate the probability of concurrency of 3 or more accident which are the same in the particular period. Is there any way to do this?
This is the best webpage on the Birthday Paradox that I’ve found!
We are doing an elementary school “science” project. We picked the Birthday Paradox and did 40 trials (using mostly the internet) and came out with the expected (though counter-intuitive) result of about 50% pairs.
Now we’ve gotten to writing the “conclusion” of the report and realize that the answer involves apparently college-level math! Question: is there a simplified way to explain the paradox, at least to hint at why it works, that a smart elementary school student could understand?
Thanks!
Hi Chris! Yep, for about 10,960 athletes you’d expect 10960 / 365 ~ 30 birthdays per day. In a room (or specific event), you can use the formula to figure out the chance of at least two people having a common birthday. If a track heat has 12 people, there’s a 16% chance of two people having the same birthday (see the formula at the bottom, but it’s 1 - e^(-12*11/(2 * 365)).
@Jamal: Interesting way to think about it – breaking it down by birth “day” and then birth “month” (might be easier to see how common it is).
@roy: Thanks, glad you liked it! Wow… there should be a name for that, virtual twin :).
Went through entire grade school without anyone sharing my same birthday?
elementary K-6
secondary 7classes twice a year for another 6 years.
Some explain the chances of that happening?
The math is slightly flawed in the respect that there are actually 366 days/year during leap years. Very interesting though… 
-d
@Shambhu: Yep, that works! But it’s a pain to compute manually. The formula in Appendix A gives a shortcut vs. having to do all those 23 multiplications out.
THis is great your the bomb man, how did you figure this our, science fair project here we go
i’m doing the project too
When I was in 7th grade my science teacher bet that there weren’t 2 people in our class of about 30 people who had the same birthday. We laughed our butts off at him because right away we had a set of twins in the class. Even once we removed them we all said our birthdays and we found the set of twins, me and a guy who all had the same birthday (Aug 3). There was also another pair of unrelated people who had the same birthday.