The birthday paradox states that within a set of 23 people (a classroom, for example) the probability that two of them have the same birthday is 50.7%

It is likely that few have heard of the birthday paradox. This refers to a mathematical approach which establishes that within a group of 23 people, the probability that two of them will have the same birthday is 50.7%.

This percentage tends to be higher as the number of people increases, reaching almost 100% in the case of a group of 365 or 366 people (taking into account whether it is a leap year).

It is worth mentioning that this approach is a paradox due to the fact that it is a mathematical truth that opposes common intuition. This means that, within the paradox, when asking for an estimate of the minimum number that a group should have so that the probability that two people in the same group coincide on the birthday date, most fail completely in this task.

Based on this premise, the developers of a website called Brain Fest took the initiative to recreate the birthday paradox, adding to it buttons that allow the user to alter certain variables.

In that sense, the user can have the possibility to increase or decrease the amount of people in each room by clicking on the buttons represented with the symbol (+) or (-) in the People area.

By clicking on the Generate room option you can set the dates for all people under a number ranging from 1 to 365, i.e. one year.

Once the results are displayed, they will be shown in colors, with red being used to represent when the dates do not repeat and green for those that coincide.

Also, by clicking on the Sample button you can generate random samples, whose number you can increase or decrease in multiples of 10 by clicking on the (+) or (-) button located on both sides of the box.

At the bottom right of the screen you can see panels with data expressing the cumulative and average of the generated results.

As the number of people in the room increases, the probability that two people were born on the same date becomes much higher.

Once you understand the dynamics that govern this paradox, it will be easy to distinguish its principles in other situations where coincidences occur that at first glance seem incredible, but when you analyze them you may notice that their occurrence is more likely than you imagine.


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