A somewhat unexpected property of randomness is that it forms patterns. Many years ago back when I was writing for Game Developer Magazine, I investigated how to automate the creation of virtual landscapes covered with trees. If the positions of the trees were truly random then inevitably there would be a few clusters of trees that were very close together, and empty spaces between the trees. Here's a perfectly random example i generated from random numbers. Notice there are clusters.
This is known as the Clustering Illusion, defined on Wikipedia as:
Something that arises from the clustering illusions is the Texas Sharpshooter Fallacy. This is sometimes deliberate practice of drawing a ring around a random cluster, and then claiming some significance to the fact that there's a lot of points in that cluster. The name comes from a joke about a Texas Cowboy who shoots at the side of a barn. His aim is poor, so there a random scattering.
He goes over to the barn and picks the biggest clusters of shots, and then paints targets centered on those clusters. So now it looks like he's been aiming for that region, and hence there's a reason for this cluster. But all he did pick one random cluster that looked good for him.
Recently there have been new stories about a cluster of deaths of US tourists in the Dominican Republic. Nine Americans have died there over the last 12 months. The causes of these deaths are mostly listed as being heart attacks. However, there have been questions raised about possible poisoning of some sort.
Could this be a clustering illusion? Heart attacks are somewhat randomly scattered through the population, and they also correlate to demographic factors, so there's going to be both real and illusory clusters. Could it be that the Dominican Republic is simple the place that had a random cluster of deaths this year?
Perhaps there's something else at play here - the Baader-Meinhof phenomenon, also called the Frequency illusion. This is a trick your mind plays on you where if you've just recently heard of something, or it's otherwise in your thoughts, then you start to notice it occurring more frequently. The classic example is buying a new car (or just reading about a type of car, like a Tesla), and then you start to see them more often. They are not actually any more common, but you just notice them more.
So perhaps the media, being primed with the idea that there's a suspicious series of deaths in the Dominican Republic, is suddenly noticing things that would have escaped their notice entirely last year. People have died of heart attacks, and even of alcohol poisoning, in the Dominican Republic before, and they will again. Is it actually any more common this year?
Now, we know that 2.7 million US citizens visit the Dominican Republic every year. We know that people die somewhat randomly from heart attacks. Each year around 325,000 adults die of sudden Cardiac Death, which is about 1/1000th of the US population of 327,000,000. Simply extrapolating, that means each year 1/1000th of the 2.7 million people who visit the Dominican Republic will die of sudden heart attacks. That's 2,700 people. If the average trip length is seven days then that means, all things being equal, we'd expect about 52 US tourists per year to unexpectedly drop dead of a heart attack in the Dominican Republic!
It's probably not that high, as people traveling abroad are usually healthier on average than people. But still, a significant number of individually unexpected deaths are to be expected over a year.