On many occasions, probability theory has had its day in court. In recent times, the use of probability concepts has typically been connected with DNA analysis that matches an individual's genetic code sequences to samples taken from a crime scene. Some scientists, including Ranajit Charkraborty of the University of Texas and Kenneth Kidd of Yale, argue that DNA evidence is about as perfect as anything can ever be. As they see it, the odds are 738

10
12
to 1 against a match by pure chance. No reasonable doubt here. Yet other experts, including Eric Lander of MIT and Richard Lewontin of Harvard, argue that subgroups of the total population, notably blacks and Hispanics, contain frequent DNA similarities, which makes the probability numbers very different, indeed. As they see it,
DNA analysis cannot be trusted.
In addition, the use of probability numbers in court has been criticized because lawyers have misused the laws of probability. Two famous cases stand out. In both cases, the special multiplication law was applied (even though the events in question were not independent) when the general multiplication law should have been applied.
The Trujillo Case. In 1946, a police officer was shot to death. Joseph Trujillo was charged with the murder. The prosecutor argued that 11 matching fibers were found that apparently had been transferred between the victim's and the defendant's clothing. The probability for one accidental fiber match was given as 0.1; hence, that of 11 matches was calculated by the special multiplication law as (0.1)
11
or a tiny 0.00000000001.
Finally, the prosecutor also noted five matching characteristics between the bullet that had killed the victim and the pistol that belonged to the defendant:
1.
Both were of 0.38 caliber, a probability given as 0.2.

2.
Rifling was right-handed, a probability given as 0.5.
3.
Both pistol and bullet showed five lands and grooves, a probability given as 0.2.
4.
Both pistol and bullet showed the chamber out of line with the barrel, a probability given as 0.2.
5.
The pistol was not, and the bullet had not come from, an automatic revolver, a probability given as 0.5.
Again, the prosecutor multiplied together the estimated probabilities to show the small joint probability of all these events and, hence, the tiny likelihood that someone else could have been the killer.
Trujillo was convicted and executed. No thought, apparently, was given to whether the stated events were independent (and hence whether the special multiplication law was even applicable). Some 18 years later, however, a similar case had quite a different outcome.
The Collins Case. In 1964, an elderly woman was mugged in an alley. Shortly afterward, a witness saw a blonde girl, her ponytail flying, run out of the alley, get into a yellow car driven by a bearded black man with a moustache, and speed away. Eventually, the police arrested Janet and Malcolm Collins, a married couple who fit the physical description given above and who also owned a yellow Lincoln.
Once again, the prosecutor invoked the laws of probability. He suggested to the jury probability values:
1.
for being a blonde of p = 0.33
2.
for wearing a ponytail of p = 0.10
3.
for being an interracial couple of p = 0.001

4.
for owning a yellow car of p 0.10
5.
for wearing a moustache of p 0.25
6.
for being a black man wearing a beard of p = 0.10
He multiplied the numbers to produce a joint probability of 0.00000008 that another couple exactly like the Collinses could have been present on the morning of the crime.
The jury, overwhelmed by the logic of it all, found them guilty beyond a reasonable doubt. Malcolm Collins received a sentence of "one year to life"; Janet Collins received a sentence of "not less than one year."
Yet a few years later, the California Supreme Court overturned the verdict. There was no evidence, it said, that the individual probability values were even roughly accurate. Most important, the factors listed above were not clearly independent of one another, as they must be to satisfy the probability law that was applied. The fact that the black man had a beard, said the court, was not independent of the fact that the couple was interracial, for example. Indeed, the court used the very technique applied in Application 8.5, The
Miracle of the Matching Birthdays , to show that there was a 41 percent chance that at least one other couple in the area might have had the admittedly unusual characteristics listed above.
Sources : Adapted from Tim Beardsley, "Pointing Fingers: DNA Identification is Called
Into Question, " Scientific American , March 1992, pp. 26-27; Darrell Huff, How to Take a Chance (New York: W. W. Norton, 1959), pp. 138-140; Time, January 8, 1965, p. 42, and April 26, 1968, p. 41; and W. Fairley and Frederick Mosteller, "A Conversation
About Collins," University of Chicago Law Review, 1974.