Never let it be said that probabilities don't matter. Sally Clark, a British woman whose two sons suffered cot death (a.k.a. SIDS), was arrested under suspicion of murder. Her prosecution included testimony from Roy Meadow, a pediatrician who claimed that the probability that both sons died of natural causes was less than 1 in 72 million. He got that figure by squaring the 1 in 8500 likelihood of cot death in affluent families.He irresponsibly ignored the requirement that events be independent for his calculations to yield meaningful results.
Furthermore, his results imply that there was only a 13 billionth of a percent chance that Mrs. Clark was not a murderer, apparently assuming that it was improbable even for the first son to die. With probability, it's extremely important that the "clock" be started exactly with the surprising event, never including previous "related" events. If the Pick 3 numbers for one day are 1-9-6, that's not surprising. If they're also 1-9-6 the next day, it is surprising. So if the odds are 1-in-1000 for winning, the probability telling us how surprising our "coincidence" is would be closer to 1-in-1000 (the odds of getting 1-9-6 the second day) rather than 1-in-1 million (the odds of getting 1-9-6-1-9-6) since it wasn't surprising in the least until the second 1 popped out. In the same way, nothing was surprising in Sally Clark's case until the second son died, so even without considering the other error she would only have a 1-in-8500 surprise value.
There may have been other evidence involved, but it's horrifying that someone so careless with evidence would be involved in a murder trial.
She served more than three years in prison before she was released on further evidence.
4 comments:
I added this post before the "shocking" news came out that the Nebraska Pick 3 chose 1-9-6 two nights in a row, but I weaved some details about it into the post because (a) it clarifies the point with real numbers and (b) it shows how common the mistake is. There were several news articles reporting "1-in-a-million odds" for the event, but they didn't mention that it's happened twice before and there have only been 3+ years of drawings (about 1100).
Bonus points for anyone who can figure out why it's not surprising at all that 1-in-1000 odds have been met 3 times in less than 3000 trials.
I give... tell me the answer, even if I don't get bonus points.
I give... tell me the answer, even if I don't get bonus points.
Because the Nebraska Pick 3 has been cherry-picked from hundreds of state lotteries. I'm sure it hasn't happened at all in some states, which would be just about as surprising.
The odds of hearing about a lightning strike on the news are much higher than the odds of being struck by lightning. That's pretty much the sole purpose of the news.
BTW, this has happened in other states, too (e.g. North Carolina).
I also added up the numbers on this wiki article and found that there's a total of 84 state lotteries, so my guess of "hundreds" wasn't too far off (for our purposes).
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