All your Bayes belong to us
Risk management deals with the losses that accompany uncertain events. To find the risk associated with a particular event, you multiply the probability of the event happening by the loss that the event would cause. So an event that causes $1 million is loss but happens with only a 0.1 percent chance represents $1,000 in risk.
In some cases, parts of a population can have a much greater chance of experiencing a particular event than others. This can lead to misleading ideas about risks. In some cases, conditional probabilities give a better understanding of risks.
It’s commonly believed, for example, that it’s safer to fly on a commercial airline than to drive your car to an airport. You can get this result by using the average number of fatalities per mile for travel by car and travel by airplane to estimate the chances of being killed on each trip. A closer look at the data, however, shows that a significant number of deaths in cars are caused by young, drunk men who are driving late at night. Because young, drunk men tend to not be on the road when people driving to airports are on the roads, it’s actually much safer for them. People driving to airports are also typically not young, drunk men. So the more relevant probability in this case is the probability of being killed in a automobile accident given that you’re the kind of person who would actually be traveling to an airport. Based on this conditional probability, it turns out that air travel is actually more dangerous than driving.
Gregory Baer’s book Life: the Odds gives some interesting examples of conditional probabilities, although he doesn’t call them that. For example, there are roughly 250 New York Times best-sellers each year and there are roughly 6.7 billion people in world today. If you look at the chances of writing an New York Times best-seller as being about 250 in 6.7 billion, the chances seem fairly small.
On the other hand, suppose that your book has been published. In this case your chances of having written an New York Times best-seller are roughly 1 in 220. That’s better by a huge margin. If you relax the requirements for being a best-seller to include books on other lists, like those from USA Today and Publishers Weekly, the chances of writing a best-seller get even better. Using the broader definition, the probability of having written a best-seller, given that your book has actually been published, is more like 1 in 54.
Baer’s book is very entertaining, but it definitely isn’t too serious. It also estimates the chances of Satanic possession to be roughly 1 in 7,000 each year. That’s roughly the same as the chances of dying in an vehicle accident in the US, which is about 1 in 6,535 per year. If Baer is right, there’s a significant chance, roughly 1 in 100, that a typical person will be possessed at some point in their life. Maybe there’s a bias towards young, drunk men in this estimate also.