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: