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CHARLES RICHARD SMITH has learned the hard way that you can prove almost anything with statistics. In 2009 a disputed statistic provided by a DNA analyst landed him with a 25-year jail sentence.

Smith was convicted of a sexual assault on Mary Jackson (not her real name) in Sacramento, California, which took place in January 2006. Jackson was sitting in a parking lot when a stranger jumped into her truck and made her drive to a remote location before forcing her to perform oral sex on him. When police arrested Smith and took a swab of cells from his penis, they found a second person's DNA mixed with his own.

The DNA analyst who testified in Smith's trial said the chances of the DNA coming from someone other than Jackson were 1 in 95,000. But both the prosecution and the analyst's supervisor said the odds were more like 1 in 47. A later review of the evidence suggested that the chances of the second person's DNA coming from someone other than Jackson were closer to 1 in 13, while a...