Why Is It So Common to Share a Birthday with Friends Meet the Birthday Paradox

Why Is It So Common to Share a Birthday with Friends Meet the Birthday Paradox

How many persons are you acquainted with? How many of them have the same birthday as you? In most cases, the figure is bigger than you may assume. This is common in student classrooms when at least a few youngsters in a group of 20 to 30 share a birthdate.

The birthday dilemma, also known as the birthday paradox, arises from the fact that with 365 days in a year, you would assume it would take over 100 individuals to discover someone with the same birthdate. You already have higher odds than tossing a coin with just 23 individuals.

We are worried that like the notorious Monty Hall dilemma another situation that necessitates counter-intuitive probability. Let us begin with only two individuals. The chances of you and another random person sharing a birthdate are extremely slim (364/365 or 99.7%). If three persons are present, the chances of them all having different birthdays are (364/365)x(363/365). That is 99.2 percent likelihood.

The lower the percentage becomes as more individuals are added, but you do not need 183 persons to reach 50%. When just 23 persons are involved, the method above yields a chance of 49.3 percent.

Assume you are on a game show and have three doors to choose from, a beautiful new automobile hidden behind one door, while goats hidden behind the other two. The object of the game is to choose a door and see what is behind it. Now, goats are beautiful creatures, but you really want that automobile, so you choose door number one. 

The Monty Hall Problem is a thought experiment that has sparked a lot of debate in the math community over the years. It was first published as a letter to the editor in the American Statistician in 1975, but it truly took off in 1990, when Parade writer Marilyn vos Savant asked to write it for her “Ask Marilyn” column by a reader.

Therefore, in a group the size of a classroom or a work team, the chances of sharing a birthdate are larger than a coin flip. If you have 41 employees in your workplace or department, the chances of having a birthday with someone else go to almost 90%. It is above 99 percent with 60 individuals. 

There is a 99.99997 percent probability that two persons in a group of 100 share the same birthday. Small gatherings are excellent if you do not enjoy sharing your birthday.