The men's sister had still another theory entirely. ''She worried that it was a plot to kill both of them,'' the nephew says, describing his aunt's concerns that terrorists might have made their way to Raahe. ''She was angry. She wanted to blame someone. So she said the chances of this happening by accident are impossible.''

Not true, the statisticians say. But before we can see the likelihood for what it is, we have to eliminate the distracting details. We are far too taken, Efron says, with superfluous facts and findings that have no bearing on the statistics of coincidence. After our initial surprise, Efron says that the real yardstick for measuring probability is ''How surprised should we be?'' How surprising is it, to use this example, that two 70-year-old men in the same town should die within two hours of each other? Certainly not common, but not unimaginable. But the fact that they were brothers would seem to make the odds more astronomical. This, however, is a superfluous fact. What is significant in their case is that two older men were riding bicycles along a busy highway in a snowstorm, which greatly increases the probability that they would be hit by trucks.

Statisticians like Efron emphasize that when something striking happens, it only incidentally happens to us. When the numbers are large enough, and the distracting details are removed, the chance of anything is fairly high. Imagine a meadow, he says, and then imagine placing your finger on a blade of grass. The chance of choosing exactly that blade of grass would be one in a million or even higher, but because it is a certainty that you will choose a blade of grass, the odds of one particular one being chosen are no more or less than the one to either side.

Robert J. Tibshirani, a statistician at Stanford University who proved that it was probably not coincidence that accident rates increase when people simultaneously drive and talk on a cellphone, leading some states to ban the practice, uses the example of a hand of poker. ''The chance of getting a royal flush is very low,'' he says, ''and if you were to get a royal flush, you would be surprised. But the chance of any hand in poker is low. You just don't notice when you get all the others; you notice when you get the royal flush.''

When these professors talk, they do so slowly, aware that what they are saying is deeply counterintuitive. No sooner have they finished explaining that the world is huge and that any number of unlikely things are likely to happen than they shift gears and explain that the world is also quite small, which explains an entire other type of coincidence. One relatively simple example of this is ''the birthday problem.'' There are as many as 366 days in a year (accounting for leap years), and so you would have to assemble 367 people in a room to absolutely guarantee that two of them have the same birthday. But how many people would you need in that room to guarantee a 50 percent chance of at least one birthday match?

Intuitively, you assume that the answer should be a relatively large number. And in fact, most people's first guess is 183, half of 366. But the actual answer is 23. In Paulos's book, he explains the math this way: ''[T]he number of ways in which five dates can be chosen (allowing for repetitions) is (365 x 365 x 365 x 365 x 365). Of all these 3655 ways, however, only (365 x 364 x 363 x 362 x 361) are such that no two of the dates are the same; any of the 365 days can be chosen first, any of the remaining 364 can be chosen second and so on. Thus, by dividing this latter product (365 x 364 x 363 x 362 x 361) by 3655, we get the probability that five persons chosen at random will have no birthday in common. Now, if we subtract this probability from 1 (or from 100 percent if we're dealing with percentages), we get the complementary probability that at least two of the five people do have a birthday in common. A similar calculation using 23 rather than 5 yields 1/2, or 50 percent, as the probability that at least 2 of 23 people will have a common birthday.''

Got that?

Using similar math, you can calculate that if you want even odds of finding two people born within one day of each other, you only need 14 people, and if you are looking for birthdays a week apart, the magic number is seven. (Incidentally, if you are looking for an even chance that someone in the room will have your exact birthday, you will need 253 people.) And yet despite numbers like these, we are constantly surprised when we meet a stranger with whom we share a birth date or a hometown or a middle name. We are amazed by the overlap -- and we conveniently ignore the countless things we do not have in common.