The book coins an acronymical term, Petwhac (Population of Events That Would Have Appeared Coincidental). This is defined as all those events that may be considered to be a 'coincidence' if studied casually, but are both possible and statistically probable.
A way to get an idea of how to use the petwhac is as follows. Say you see a friend from school you have not seen for years when you are on holiday (an unlikely event); before saying it is fate or coincidence, think what is in the petwhac (meeting any friend from the same time period at least, friends of your brothers, sisters or parents, old flames, neighbours, teachers, someone who worked in the local chip-shop... the list is probably endless, and all would seem coincidental). In short: the bigger the petwhac, the stronger case you have to avoid ascribing something to fate or coincidence.
Dawkins offers several examples of petwhacs in the book, two of which are the bedside clock of a woman (Richard Feynman's wife) stopping exactly when she died, and a psychic who stops the watches of his television audience.
The first is explained by the fact that the clock had a mechanical defect which made it stop when tilted off the horizontal, which is what a nurse did to read the time of death in poor lighting conditions. The matter of the watches, in Dawkins' own words, is explained thus —
If somebody's watch stopped three weeks after the spell was cast, even the most credulous would prefer to put it down to chance. We need to decide how large a delay would have been judged by the audience as sufficiently simultaneous with the psychic's announcement to impress. About five minutes is certainly safe, especially since he can keep talking to each caller for a few minutes before the next call ceases to seem roughly simultaneous. There are about 100,000 five-minute periods in a year. The probability that any given watch, say mine, will stop in a designated five-minute period is about 1 in 100,000. Low odds, but there are 10 million people watching the show. If only half of them are wearing watches, we could expect about 25 of those watches to stop in any given minute. If only a quarter of these ring in to the studio, that is 6 calls, more than enough to dumbfound a naïve audience. Especially when you add in the calls from people whose watches stopped the day before, people whose watches didn't stop but whose grandfather clocks did, people who died of heart attacks and their bereaved relatives phoned in to say that their 'ticker' gave out, and so on.
Dawkins defends his choice of the word "population" by writing "Population may seem an odd word, but it is the correct statistical term.", adding "I won't keep using capital letters because they stand so unattractively on the page."
Read more about this topic: Unweaving The Rainbow