Jon Baron’s post on interpretation of coincidences reminded me of some similar observations about coincidences by B. F. Skinner. Baron, who’s research I admire greatly, discusses how people’s explanations for coincidences are predicated on faulty comparisons of two conditional probabilities: One is the hypothesis that there is some force (e.g., a god) acting to cause coincidences, and the other is that a coincidence is simply a specific instance of surprise, ignoring many other equally probable instances.
Skinner’s discussion of coincidence does not depend on the explicit statement of probabilities that Baron used, but it includes a very similar fundamental notion. He argues that people live in “an extremely complex sample space” where any given event is just about as likely to occur as any other given event in the same event group. The probability of being dealt a hand of 13 cards (from an honest deck of 52 cards) all of which are hearts is just one of the ~635 billion possible specific arrays of 13 cards; but we remark on how odd such a deal is.
I’ve found myself thinking about these ideas when I have a bill at a check-out register that totals an even dollar amount (e.g., $11.00). Given that so many items are priced at $x.99, I have to suspect that the probabilities differ across the range from $x.00 to $x.99 for totals at registers. Someone who has better math skills than I could probably model this.
I shan’t however, submit to the notion that a god made my receipt show a particular amount.