Coincidence or Probability? 

Thompson, Keith. Coincidence?. 2022

Over the last couple of weeks, several of my friends have shared stories with me about specific coincidences they experienced and their take on dissecting their meaning. This, in turn, led me to start questioning my own beliefs when it comes to coincidences. Personally, I have never been a particular believer in coincidences; in fact, I easily argued back against my friends’ theories that one could definitely calculate the probability of those events happening to them then and there. I admit that some of them are mathematically harder to explain than others, but I still believed that essentially everything could be boiled down to statistics and probability. I tried to recall any interesting coincidences that have happened to me so I could analyse the topic for this article, but since I could not remember any, I procrastinated a great deal and decided to work on it at the airport as I waited for my flight home, and funnily enough, a coincidence happened just then. 

I was scrolling through Instagram stories as I waited to board my flight when I came across one from someone who was in the year below me back in high school, whom I had not spoken to in roughly three years, who happened to post that he was also at Schiphol. I replied to him saying I was also there, but once I looked up from my phone, I found him there in the boarding line for the same flight. We picked up small talk and joked around saying what a coincidence it was that we were on the same flight, especially considering that I had nearly taken the one the night before instead. We discovered that our seats were just behind each other, and when we boarded the plane, I saw a girl from my high school year sitting in the row next to mine, whom I also had not spoken to in years. This was also surprising, and as we began to joke about it, yet another good friend of mine from high school entered the plane! What are the odds that the four of us were on that same plane, that specific date and time, considering we were in the middle of the university block and had never bumped into anyone we knew at the airport?  

Most people would consider this a coincidence. My friends on the flight certainly did. However, I would argue against it. I genuinely believe that it comes down to probability. Unfortunately, my grasp of maths and statistics is a little too limited for me to calculate the probability of us taking the same flight, but I can think of a couple of factors that influenced this: we all live in Amsterdam, we all have family living in Portugal, that particular flight was more convenient than the usual 6 am flight, and we were all going for a short weekend trip to visit our families as we were nearly finished with our midterms. Surely if you consider all of these factors (and possibly a few more that I did not think of), you can calculate the probability of this event taking place. This really piqued my interest, so I began to research a little more about the mathematics behind coincidences and I discovered that most statisticians and psychologists have tried to explain these meaningful events through various theories, such as Carl Jung’s synchronicity study, David Spiegelhalter’s collection of most frequent coincidences, and Ruma Falk’s study on coincidences and egocentrism. However, in this article I will be focusing on the Law of Really Large Numbers, frequency illusions and premonitions, and different beliefs, which are the most well-known and largely accepted theories. 

The most common explanation, the one which I personally believe in, is that coincidences only happen because we notice them. Any event in our lives has the power to generate a coincidence, we simply don’t notice them as they are mostly too boring to feel meaningful and thus do not grab our interest. In other words, if event 1 was slightly more meaningful to us, we are more likely to pay greater attention to similar situations, and thus event 2 will seem like a coincidence. However, both events were bound to happen independently. I would have taken that Thursday flight regardless of whether my other friends had also chosen to take that flight. A theory that goes hand-in-hand with this line of thought is that of the Law of Really Large Numbers. This law states that as the sample size grows, its mean gets closer to the average of the whole population as a result of the sample being more representative of its entire population. It is a principle of probability which describes that the frequency of events with the same likelihood even out if given enough opportunities. In simpler terms: crazy things are more likely to happen if given a large enough sample. In fact, this is where the birthday probability comes from: in a sample size of only 23 people, there is a 50/50 chance that at least two of them will share the same birthday, and the probability shoots up to about 90% if one considers it a coincidence of them being within a day of each other. You can easily apply this law to your own life: consider all the places you usually go and all the places the people you know usually go – chances are you will run into someone, somewhere, at some point. Nevertheless, you will think it is a coincidence when it does happen. 

Another explanation revolves around those coincidences in which you think of someone and shortly after you receive a call from them, or when you learn a new word and then suddenly you see it everywhere. Statistician David Spiegelhalter considers these to be Mind-Environment coincidences, which can be described as premonition-esque. These are the kind of things that makes it seem like what’s in our minds seeps into the world, but although it makes it less interesting, I believe these are not specifically created by the world around us, but rather by what we pay attention to. The times we think of someone and do not receive a call or text from them far exceed the times in which that does happen, but we don’t notice them because they are not surprising or interesting to us. Linguist Arnold Zwicky describes this theory as the frequency illusion, which suggests that when your brain takes notice of something once, it becomes more primed to notice it again. Next, there are the Mind-Mind coincidences, which are more challenging to explain. These would be like a twin feeling phantom pain that their twin experiences physically, or a mother having a gut feeling that something is happening to her children. These blurs the line between science and synchronicity, representing the strong connection between two individuals. Finally, there are Environment-Environment coincidences, which are a series of events that happen in the physical world, making them easier to grasp for they are more objectively observable. Me bumping into several people from my high school on the same flight falls into this category. 

Photo credits: UC Denver, What Is The Frequency Illusion  

Despite there being several different explanations and studies on various types of coincidences, most of them seem to agree that they are found in the eye of the beholder: if no one sees it, it is not a coincidence. These events physically take place all the time, but what makes them a coincidence is that we actually acknowledge them. Furthermore, humans are extremely good at finding patterns. As a matter of fact, this is how we process the underlying order and structure of reality – we create a network that connects everything and everyone. We look for patterns everywhere; through this, we come to understand our world a little better and, to a small degree, even control it. We know that if we flip a light switch, a lamp will turn on. Subconsciously, we filter out the importance of events through what we consider chance – we dismiss everything we consider to have happened by chance and take particular notice of the events that feel predetermined. This sorting of experience allows us to define coincidences as the by-product of our brains’ meaning-making system and act on the most meaningful events. 

Although I don’t believe that coincidences really exist and everything can be explained through mathematics and psychology, I find this to be a rather boring way of experiencing life. We get so much joy from the situations we consider as serendipity or fate and the surprise factor is so endorphin-boosting that it feels almost bleak to think that the universe doesn’t work in mysterious ways or that certain events are not destined to happen in order for you to find your purpose in life. It’s much more exciting to believe that meaningful, rare events happen to us in order to give us unique experiences and enrich our lives. The exploration of this chaotic collection of curiosities and significant events makes life so much more enticing. For example, the night before I (finally) sat down to write this article, I decided to join a friend’s group to watch a football match and was afterwards invited to hang out at a nearby bar for a bit, and strangely enough, I was recognised by someone I see every morning at the gym. Coincidence? Statistically, probably not. Essentially we were both in a club relatively close to our mutual gym on a Friday night with a group of friends and we only picked up a conversation because the club was rather dead. On top of that, the coincidence itself is not that we were there simultaneously, but rather it is the fact that he recognised and spoke to me. But of course, the story is much more intriguing if we don’t calculate the probability of this happening. Thus, I much rather go through life collecting positive coincidences that make for engrossing stories than reduce life experiences to probability. As interesting as it might be to understand how our brains make these sorts of connections and selections, life is too short to dismiss surprising events into statistics.  

Written by Laiana Farias


Hand, David. The Improbability Principle: Why Coincidences, Miracles, and Rare Events

Happen Every Day. First Edition, Scientific American / Farrar, Straus and Giroux, 2014.

Shamdasani, Sonu. Synchronicity: An Acausal Connecting Principle. (From Vol. 8. Of the

Collected Works of C. G. Jung). Princeton UP, 2019.

Falk, Ruma. “Judgment of Coincidences: Mine versus Yours.” The American Journal of

Psychology, vol. 102, no. 4, 1989, pp. 477–93. JSTOR, Accessed 4 Dec. 2022.


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