Another mathematical notion which could have been used more trenchantly was that of statistical independence. The definition: two events are statistically independent if one's occurring doesn't affect the likelihood of the other's occurring. Furthermore, when two happenings are independent, the probability of their both occurring is simply the product of their respective probabilities. Imagine flipping a coin twice. The outcomes of the two flips are independent, and so the probability of obtaining two heads is 1/4 - the result of multiplying 1/2, the likelihood of a head on the first flip, by 1/2, the likelihood of a head on the second flip. Similarly, the probability of obtaining three consecutive heads is simply 1/8 - 1/2 x 1/2 x 1/2, and so on.
If the various bits of incriminating evidence were independent manifestations (and many were), then their respective probabilities should be multiplied to obtain the probability of all of them turning up. Forget DNA momentarily, and consider only the probabilities of two simple physical findings. What is the likelihood that the perpetrator's footprints leading from the crime scene would be size 12, Mr. Simpson's size? And what is the likelihood that Mr. Simpson would sustain a cut on the left side of his body the very night the murderer did (judging from the blood spots to the left of the footprints)? Estimates for these probabilities may vary, but let's be generous and say that they're as high as 1 in 8 and 1 in 500, respectively. The probability of both these independent pieces of evidence turning up is the product of their probabilities - 1 in 4,000, a very strong indicator of guilt completely separate from the overwhelming DNA evidence. Bringing in the many other bits of evidence further reduces this tiny probability.
Independence played a role in the DNA testimony as well where citations of probabilities smaller than 1 in 5.7 billion (the earth's population) were wrongly viewed by many as instances of prosecutorial exaggeration. But the earth's population has nothing to do with the matter. Since there are incomparably more potential DNA patterns than there are people on earth, it makes perfectly good sense to assert that the probability that someone has a particular fragment is, say, 1 in 75 billion (the latter figure the result of multiplying many small probabilities together).
Of course, there are also exculpatory probabilistic arguments. It can be contended, for example, that the crucial question in the trial was not the probability of an innocent person's having all this evidence arrayed against him, but the probability of a person with all this evidence arrayed against him being innocent, which is a quite different thing. In the Simpson case, however, this is not a very promising tack to take, and so the defense was left with their theory of conspiracy and coverup. Attaching a precise probability to this scenario is not possible, but accepting it entails believing that the same bungling police department that cavalierly ignored all of Nicole Simpson's previous calls for help could and would, upon discovering her death, instantly and without direction devise an elaborate frame-up of Mr. Simpson. Police officers, lab technicians, and criminalists (about whom, with one exception, no evidence of moral monstrosity was presented) would have had to be implicated in a complicated network of villainy.
Much more can be said, but many feel that statistics are boring and that we should therefore pardon statisticide. Perhaps, but not when it also leads to the pardoning of homicide.
Professor of Mathematics at Temple University, John Allen Paulos is the author of Innumeracy and, most recently, of A Mathematician Reads the Newspaper.