It’s laughable sometimes how poorly statistics are interpreted. I see it all the time in the media especially, but your average Joe isn’t exactly a stats genius either. Here’s a pretty good excerpt from an report published by Jessica Utts of the University of California, Davis about Probable Coincidences.
PROBABLE COINCIDENCES
Most people have experienced one or more events in their lives that seem to be improbable coincidences. Some such events are so surprising that they attract media attention, often with estimates of how improbable they are. For instance, Plous (1993) reported a story in which a Mr. and Mrs. Richard Baker left a shopping mall, found what they thought was their car in the parking lot, and drove away. A few minutes later they realized that they had the wrong car. They returned to the parking lot to find the police waiting for them. It turned out that the car they were driving belonged to another Mr. Baker, who had the same car, with an identical key! Plous reported that the police estimated the odds at a million to one. The problem with such stories and computations, is that are based on asking the wrong question. The computation most likely applies to that exact event happening. A more logical question is, what is the probability of that or a similar event happening sometime, somewhere, to someone. In most cases, that probability would be very large. For instance, I was once on a television talk show about luck, with a man who had won the million dollar New York State lottery twice, and the host of the show thought this demonstrated extraordinary luck. While it may have been wonderful for that individual, Diaconis and Mosteller (1989) report that there is about an even chance of the same person winning a state lottery in the United States in a seven year period. That was precisely the interval between the two wins for this person. Remember that there are over six billion people in the world, with many circumstances occurring to each one daily. Therefore, there are surely going to be some that seem incredible. In fact if something has only a one in a million probability of happening in a given day, it will happen, on average, to over 6000 people in the world, each day. When the media reports an incredible coincidence, psychic prediction, and so on, it should be viewed from this perspective.



















