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Please Help Me Understand the Birthday Paradox!


I was at a small New Year’s Eve party a few years back and realized that of the forty guests at the party, four of us had the same birthday. All four of us were women, none of us was born in the same decade, and none of us truthfully matched the specifications of our astrological sign (Gemini, if you must know).

 

I looked up the “Birthday Paradox” to find out the down-low on the statistic and found out that if twenty-three people are together (or are grouped randomly together whether they are in the same room or not), there is a 50% chance that at least two of the people will share the same birthday.

 

 

This isn’t the first time I’ve heard the same number and have heard of the “Birthday Paradox” before. For a change, I decided to challenge my mathematical abilities (which truthfully haven’t been used since high school) to understand the math behind the probability. (Anyone adept at math should immediately proceed to this page which is full of graphs and strange equations explaining the phenomenon in intricate detail.) 

 

The simplest explanation for why this so-called birthday paradox works is HERE—the writer advises “flipping the problem to find out the odds for everyone having a different birthday”. In addition to the explanations and “possibility equations” given on the site, there is actually a birthday calendar which can help you calculate the possibility of a shared birthday or what I like to call a “birthday surprise”—not to be confused with a “birthday treat”, which is of course, chocolate cake. 

 

The strange thing for me about the “Birthday Paradox” is that I don’t remember ever once sharing my birthday with a classmate all the way through elementary school. (Obviously, since there were some of the same students each year in my classes, this is to be expected, but I was in a combined class with ninety students in 6th grade and no one had my birthday. According to the Birthday Calculator on the site, the odds look to be about a 100% that I would share my birthday with a classmate.)

 

I can understand the equations on the page if I concentrate, but I am still unsure how they work out in real life. This is where the SMART people (like you!) come in to help me. How is this even possible? Is the Birthday Calendar flawed somehow? Do the birthday statistics hold up for you? Of your Facebook friends, how many of them have the same birthday?

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Photo Credit: Flckr Beautiful Freaks