Chapter 1: Introduction to Probability

Life's most important questions are, for the most part, nothing but probability problems. - Laplace

In 1968 a jury found defendant Malcolm Ricardo Collins and his wife defendant Janet Louise Collins guilty of second degree robbery. The decision hinged on the testimony of bystanders, which stated that the perpetrators had been “black male, with a beard and moustache, and a caucasian female with blonde hair tied in a ponytail,” and that they escaped in a “yellow motor car.” A mathematician testified that the odds against this couple being innocent were one in twelve million, and this was enough for the jury to convict. Later, in an appeal, the California Supreme Court reversed the decision primarily because of lack of evidence, and faulty inference.

In another case, Sally Clark was convicted in 1999 of the murder of her two young sons. Again, the testimony hinged on a statistical argument - the chances of one baby dying in their bed 1 in 8500, so therefore the chances of two of them dying in the same way is the square of this, or 1 in 73 million. Several years later, and a public statement from the Royal Statistical Society highlighting the erroneous logic, Sally Clark was released - although she never overcame the resulting damage to her life that the conviction had caused.

We will cover these cases in more detail later, and why the inference was faulty, but I introduce the stories here for two reasons. First, is to point out that there are cases in which proper statistical inference can be a life and death matter. Second, it is to highlight the fact that such inference can run counter to one's intuition. Part of the purpose of this book is to retrain your intuitions and your habits of intuition to avoid such failures.