via NeuroLogica Blog
In just about every disaster or event in which there are many deaths, such as a plane crash, there is likely to be, by random chance alone, individuals who survived due to an unlikely sequence of events. Passengers missing their flight by a few minutes can look back at all the small delays that added up to them seeing the doors close as they a jog up to their gate. If that plane were then to crash, killing everyone on board, those small delays might seem like destiny. The passenger who canceled their flight because of flying anxiety might feel as if they had a premonition.
This is nothing but the lottery fallacy – judging the odds of an event occurring after the fact. What are the odds of one specific person winning the lottery? Hundreds of millions to one against. What are the odds of someone winning the lottery? Very good.
Likewise, what are the chances that someone will miss or choose not to take any particular flight? Very high – therefore this is likely to be true about any flight that happens to crash. If you are that one person, however, it may be difficult to shake the sense that your improbable survival was more than just a lucky coincidence.
A similar story has emerged from the Sandy Hook tragedy. A mother of a kindergartener there, Karen Dryer claims that her 5 year old son was saved by his psychic powers. She reports that her son, after a few months at the school, started to cry and be unhappy at school. He was home schooled for a short time, during which the shooting occurred. Now, at the new elementary school that recently opened, he seems to be happy.
In retrospect it may seem like a compelling story – if one does not think about it too deeply. As Ben Radford points out in the article linked to above, the story as told is likely the product of confirmation bias. The mother is now remembering details that enhance the theme of the story (her son’s alleged psychic powers) and forgetting details that might be inconsistent.
Most improbable coincidences likely result from play of random events. The very nature of randomness assures that combing random data will yield some pattern.
By Bruce Martin via The Committee for Skeptical Inquiry – CSI
“You don’t believe in telepathy?” My friend, a sober professional, looked askance. “Do you?” I replied. “Of course. So many times I’ve been out for the evening and suddenly became worried about the kids. Upon calling home, I’ve learned one is sick, hurt himself, or having nightmares. How else can you explain it?”
Such episodes have happened to us all and it’s common to hear the words, “It couldn’t be just coincidence.” Today the explanation many people reach for involves mental telepathy or psychic stirrings. But should we leap so readily into the arms of a mystic realm? Could such events result from coincidence after all?
There are two features of coincidences not well known among the public. First, we tend to overlook the powerful reinforcement of coincidences, both waking and in dreams, in our memories. Non-coincidental events do not register in our memories with nearly the same intensity. Second, we fail to realize the extent to which highly improbable events occur daily to everyone. It is not possible to estimate all the probabilities of many paired events that occur in our daily lives. We often tend to assign coincidences a lesser probability than they deserve.
However, it is possible to calculate the probabilities of some seemingly improbable events with precision. These examples provide clues as to how our expectations fail to agree with reality.
In a random selection of twenty-three persons there is a 50 percent chance that at least two of them celebrate the same birthdate. Who has not been surprised at learning this for the first time? The calculation is straightforward. First find the probability that everyone in a group of people have different birthdates (X) and then subtract this fraction from one to obtain the probability of at least one common birthdate in the group (P), P = 1 – X. Probabilities range from 0 to 1, or may be expressed as 0 to 100%. For no coincident birthdates a second person has a choice of 364 days, a third person 363 days, and the nth person 366 – n days. So the probability for all different birthdates becomes: