The Counter-Intuitive Birthday Problem in Mathematics

The birthday problem in math tells us that if there are at least 23 people in a given setting, the likelihood of two of them sharing the same birthday is over 50%. This possibility is as likely as a tossed coin landing on heads. In fact, if there are 60 or more people in a given setting, there is a 99% chance that you will meet someone who shares the same birthday as you.

Ali

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Photo by Luca Upper on Unsplash

As humans, despite numerous things to fascinate us, we always become shocked when we meet someone who shares the same birthday as us. While this level of surprise may come across as understandable if you are one of two people in a given setting, it wouldn’t be so if you were one student among 23 in a classroom or one of 23 people in a cafe you’ve sat in to drink a hot chocolate or peach-mango tea, or one of the 23 people on the Argentinian national team for the 2022 World Cup.

That is because the birthday problem in math tells us that if there are at least 23 people in a given setting, the likelihood of two of them sharing the same birthday is over 50%. This possibility is as likely as a tossed coin landing on heads. In fact, if there are 60 or more people in a given setting, there is a 99% chance that you will meet someone who shares the same birthday as you.

However, this situation continues to befuddle everyone who hears of it for the first time and invokes the question, “how is that possible?” because there are 365 days in the solar calendar. It seems more likely to us that everyone’s birthday falls on separate dates. Furthermore, the probability of sharing the same birthday with one of any 22 people who enter our lives in a given instance should be utterly low in a system where there are 365 days. For instance, while the probability of a tossed coin landing on heads or tails being only 50%, it would seem that the probability of two of 23 random selections out of a possible total of 365 should not exceed 50%.

Yet, normally, the human brain has trouble with exponential thinking, and this paradox is approached…

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Ali

Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better. alikayaspor@gmail.com