What is the probability that it shakes 3 times in the same day?

On September 19, just after the drill with which the residents of the capital prepare for earthquakes and at the same time commemorate the anniversary of the 1985 and 2017 earthquakes that had devastating consequences in Mexico City, as it trembled again.

People heard the seismic alert alarm for the second time that day, but it was not just another drill, the confusion turned into disbelief and then into alarm, while schools and workplaces were evacuated to the rhythm of the buildings that were They did it once again on September 19.

Fortunately this time there would be no losses in Mexico City, from the scare and the incredible anecdote that it trembled for the third time on September 19 did not happen, all these five years after having lived the macabre coincidence that the two most devastating earthquakes in the city occurred precisely on that exact date, unfortunately closer to the epicenter located in Qual Michoacán in Michoacán there would be two victims and property damage caused by the earthquake and its consequent tsunami affecting mainly the coasts of Michoacán and Colima.

Social networks were filled with jokes and memes, it is the way to deal with stressful events, but disbelief prevailed as people wondered, why today? Because on September 19th again? What were the odds of this happening?

This question had an answer that was widely disseminated on social networks, the doctor in physics José Luis Mateos believed that the probability of having three earthquakes greater than magnitude 7 in a country is one in 133225, which sounds incredibly unlikely and had the unfortunate effect of fueling conspiracy theories, if it is so unlikely that this happens naturally there must be some other explanation an artificial force causing it or perhaps a supernatural force.

But immediately the scientists specialized in statistics came to the rescue, this is explained with something that in probability theory is known as "the birthday paradox"; Imagine that you are put in a room with 22 other people, what is the probability that two people in that room plan a year on the same day? We intuitively tend to think that it is extremely unlikely, after the whole year has 365 possible days and there are only 23 people.

But in reality it is not like that, it is much more likely than it seems, this is because we tend to think of it as the probability that someone else in that room has a birthday on the same day as us, in which case if the probability is less than 6%, but in reality we must consider that among the 23 people in the room there are 253 possible combinations and this greatly increases the chances that two of those people have birthdays on the same day, in fact the probability that in a group of 23 people two of them share the same birthday is 50%.

To understand in the case of earthquakes in Mexico, let's say that in a group of 30 earthquakes, which are those that have occurred in the subduction zone of the coco plate, since the 1985 earthquake with a magnitude greater than 7 the probabilities of a triple-shared “event or birthday” is around 3%, not as likely but definitely not as incredibly unlikely as the viral stat would have us believe.

Taking into account that Mexico shakes so much, that 87 earthquakes of magnitude 7 or greater have occurred since 1900 to date, this coincidence of three occurring on September 19 is not so extraordinary, in fact, it is not even the only case of three Earthquakes occurring on the same date, in southern California, another highly seismic zone, have June 28, the date on which the 1966 Palm film, 1991 Sierra Madre and 1992 earthquakes occurred. landers.

If one investigates the statistics of complex systems such as earthquakes, one will find apparent anomalies everywhere, for example, there was a six-year period from 2004 to 2009 in which there was no earthquake of magnitude greater than 7 in Mexico and nobody says anything this is called statistical bias, we pay more attention to what we find most relevant or most entertaining or most spectacular remember that as we are.

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