People systematically misjudge coincidence because they underestimate how many opportunities for coincidence actually exist

Paulos highlights how astonished people are by coincidences, two strangers sharing a birthday, a dream that seems to predict an event, without realizing how mathematically expected such occurrences are given enough chances. He uses the classic birthday problem: in a group of just 23 people, there's better than even odds that two share a birthday, a result that strikes most people as implausible because they intuitively picture their own single birthday's odds rather than the far larger number of possible pairings within the group. This gap between intuition and calculation explains why people attribute mystical significance to events that are actually statistically unremarkable once you account for the sheer number of chances for something "coincidental" to happen across a population or over time. Psychics and pseudoscientific claims often exploit this blind spot, presenting an expected statistical occurrence as evidence of a special pattern or hidden cause. Paulos's broader point is that low-probability events happen constantly simply because there are so many of them. Takeaway: before treating a coincidence as meaningful, ask how many chances there actually were for something like it to occur.