The Prosecutors Fallacy – Intitution and the Miscarriage of Justice

Imagine the scene – you are in the final round of a TV game show. To claim your prize, you select a door from a choice of three closed doors. Two doors have a goat behind them, the other one million dollars.

You select one door – it remains closed. The host opens one of the other doors to reveal a goat and offers you the choice to choose again. Do you select the other door? OR do you stick with your original choice?

Most people choose to stick with their original choice.

When you made the initial choice, there was one chance in three of selecting the correct door. Open another door to reveal a goat does not change that. By selecting the other door, it is now a 50% chance of winning the prize – not a 33% chance.

Nearly everyone believes it does not matter.

AND it is very revealing that nearly everyone is very reluctant to change their mind once they have chosen the door.

Even after it has been explained – it can still be difficult to accept that the chances are 50% better by selecting the other door.

Imagine that there is a rare disease – it is an insidious disease – very uncomfortable and fatal disease. It affects 1 in 10,000 people. There is a test that is 95% accurate. That is, if a test is positive there is a 5% chance that is it wrong. There are no false negatives.

You have the test. The test is positive. What are the chances that you have the disease?

In a group of 10,000 people, you would expect 1 person to have the disease and 500 people to have a false positive test. That means there is 1 chance in 501 that you actually have the disease.

Our intuitive sense of probability can easily be wrong.

Misunderstanding of probability can have tragic consequences – especially in a court room.

In Los Angeles in 1968, Malcolm Collins and his wife Janet were sent to jail. An elderly lady had been robbed by a white woman with blonde hair and a black man with a moustache, who had both fled in a yellow car. The chances of finding a similar interracial couple matching that description were 1 in 12 million, an expert calculated. The police were convinced and without much deliberation so was the jury. They assumed that there was a 1 in 12 million chance that the couple were not the match and that this was also the likelihood of their innocence.

They were wrong on both counts. In a city such as Los Angeles, with millions of people of all races living in it or passing through, there could well be at least one other such couple, giving the Collinses an evens or better chance of being innocent. Not to mention that the description itself may have been inaccurate – facts that helped reverse the guilty verdict on appeal.

This error even has a name. The “Prosecutor’s Fallacy” and it is an easy mistake to make. It confuses two different probabilities. Firstly, the probability that someone is innocent if they match to a piece of evidence. This is what we need to know. However we are usually told the probability that someone is a match to a piece of evidence if they are innocent.

In the 1991 rape trial of Andrew Deen in Manchester UK, a so called expert witness agreed on the basis of a DNA sample that “the likelihood of being any other man but Andrew Deen being responsible is 1 in 3 million.”

Wrong, wrong, wrong. One in 3 million was the likelihood that any person in the general population had a DNA profile matching that from the crime scene. With around 30 million males in the UK, you could expect 10 males to match. If that was the only evidence, then the probability of Deen being innocent even though he was a match is 90%.

On the basis of DNA evidence at the original trial, Deen was sentenced to 16 years in prison for rape.

During the appeal it was heard that discrepancies in two out of the ten bands of DNA used to match Deen’s sample were not taken into account. A professor of forensic medicine from Germany said at the appeal that in his opinion the DNA evidence would have been sufficient to show Deen’s innocence, not his guilt.

Even if the 1 in 3 million figure was correct, the conclusion that the probability that Deen is innocent IS NOT 1 chance in 3 million. This is a serious miscalculation.

Deen was only exonerated after a fellow prisoner overhead another prisoner stating that he was responsible for the murder.

One tragic case involved an English solicitor, Sally Clark in England. In November 1999, she was convicted of smothering her children, Christopher and Harry, whilst they were sleeping.

Christopher died in December 1996 within a few weeks of his birth, and Harry died in similar circumstances in January 1998. A month later, Clark was arrested and tried for both deaths. The defense legal team contended that the children had died of sudden infant death syndrome (SIDS).

The prosecution case relied on flawed statistical evidence presented by paediatrician Sir Roy Meadow, who testified that the chance of two children from an affluent family suffering SIDS was 1 in 73 million. He had arrived at this figure by squaring his estimate of 1 in 8500 chance of an individual SIDS death.

Sir Roy’s statistical analysis was wrong, irrelevant, biased and totally misleading.

The Royal Statistical Society later issued a statement arguing that there was no statistical basis for Meadow’s claim and stated that it was a “misuse of statistics in the courts“.

The figure was disputed by the Society and other experts who stated that genetic and environmental factors were NOT taken into consideration and that the odds of a second cot death in the same family were closer to 200 to one.

Sally was convicted in November 1999. The convictions were upheld on appeal in October 2000, but overturned in a second appeal in January 2003, after it was revealed that Alan Williams, the prosecution forensic pathologist, who examined both babies, had failed to disclose microbiological reports that indicated that Harry had died of natural causes.

Sally was released from prison having served more than three years of her sentence. Her third child was removed from her care. She never recovered and died at the age of 42 in 2007 from alcoholic poising.

Sally was vilified by the media and the public.

The evidence that resulted in the conviction was is a consequence of the “Prosecutor’s Fallacy“.

Firstly, the incidence of an event occurring is not the same as the probability that the event will occur to a particularly person. The incidence of breast and prostate cancer is 1 in 9 – which does not mean that an individual’s chance of cancer is 1 in 9.

Both the children were boys who have a greater incidence of SIDS – approx 2/3 of cot deaths are boys. The incidence of the second baby dying of cot death is 10 to 22 times greater if the first died from cot death. Sally did have a third son on 2 November 1998 whilst the case against her was being prepared. On being sentenced, the child was removed from her care.

The prosecution argued that it is very unlikely for a double cot death to occur. Yes, but the possibility of a double infant murder is much, much less likely.

Evidence that the second child, Harry, had a streptococcus infection was deliberately withheld by the government pathologist, Alan Williams.

Williams also withheld evidence in other trials.

Both children had diphtheria, tetanus and whooping cough vaccinations with Harry’s only 5 hours prior to his death. The defense legal team declined to present this as evidence because “everyone knows” that vaccinations cannot cause SIDS and it would given the prosecution team the opportunity to dispute the evidence.

Sally was released from prison having served more than three years of her sentence. Her third child was removed from her care. She never recovered and died at the age of 42 in 2007 from alcoholic poising.

Many similar cases were reviewed as a result of Sally’s miscarriage of justice. Sally never recovered. She was found dead at her home in 2007 from alcoholic poisoning – a tragic victim of statistical ignorance and prejudice.

Our intuition is can easily be lead astray due to misinformation, prejudice and lack of understanding of basics of mathematics.

The General Medical Council struck off paediatrician Professor Sir Roy Meadow after his misleading evidence in Sally’s trial. The council him guilty of serious professional misconduct.

Sir Roy was unrepentant and had stood by his evidence.

By the time he gave evidence at Sally Clark’s trial, Meadow claimed to have found 81 cot deaths which were in fact murder but Sir Roy had destroyed the data.

In July 2005, a General Medical Council panel found Sir Roy guilty of serious professional misconduct for giving misleading statistical evidence in the trial of Sally Clark. He was subsequently de-registered.

In February 2006, Mr. Justice Collins at the High Court allowed an appeal by Sir Roy, overturning the guilty verdict and the sanction of erasure. The judge ruled that while his evidence was flawed, it did not amount to serious professional misconduct because he acted in good faith.

Sir Roy destroyed the lives of many women, men, children and their families, friends and colleagues.

The President of the Royal College of Paediatrics and Child Health (Sir Alan Craft) claimed that Sir Roy saved the lives of many children.

SO WHAT?

Cases involving Sir Roy include:

• Sally Clark: Served three years after being wrongly convicted of killing her two sons
• Angela Cannings: Served 18 months after being wrongly convicted of killing her two sons
• Donna Anthony: Served six years after being wrongly convicted of killing her son and daughter
• Trupti Patel: Cleared of killing three of her children

The chair of the General Medical Council when considering Sir Roy Meadow’s case said it was vital the public had confidence in the experts brought before the court and which is why he was de-registered.

During the trial, Sir Roy said the probability of two natural unexplained cot deaths in the family was 73 million to one.

The ruling was also subject to a statistical error known as the “prosecutor’s fallacy”.

By the time he gave evidence at Sally Clark’s trial, Meadow claimed to have found 81 cot deaths which were in fact murder but he had destroyed the data.

The panel’s chairman, Mary Clark-Glass, said Sir Roy was an eminent paediatrician but “you should not have strayed into areas that were not within your remit of expertise.”

The panel had earlier decided Sir Roy had not meant to mislead the Clark trial, but said his evidence had done so because it “erroneously implied” two natural deaths in a family would have to be independent of one another.

Giving evidence at the hearing, Sir Roy defended the calculations he used to arrive at the 73 million to one figure.

The hearing had heard testimonies from leading paediatricians in support of Sir Roy:

WHY?

He destroyed the lives of a number of families, their children, friends and colleagues.

Last updated on Friday 6 March 2026 at 01:29 by administrators