It’s not often that I get to combine my loves of mathematics and psychology, but this will be one such post.  The less mathematically inclined reader can gloss over many of the details, but the more mathematically inclined reader may refer to probability theory for further details.

The prevalence of psychopathy in the general population is believed to be anywhere from 1 in 150 individuals (Kiehl) to 1 in 25 (Stout).  Male populations have been studied in greater detail than female populations, but let’s assume that there is no difference in the proportion of psychopaths according to either dominant sex.

For a single encounter with a person, the distribution is Bernoulli in nature, so, assuming the probability is .01 (1 in 100):

[latex] P(psychopath) = p = .01 [/latex]

When meeting multiple people over the course of the day, the distribution becomes a Binomial one with parameters n, and p – the number of individuals met and the probability of any single one being psychopathic.

Those familiar with statistics will immediately recognize the following formula for determining whether x “successes” are found over n trials.

So if we meet exactly 100 people and we assume that the probability of being psychopathic is .01, the odds of meeting 1 or 2 psychopaths is:

And, via basic probability, the probability that we meet at least one psychopath is 1 – {probability of meeting no psychopaths}.

So assuming that we meet 100 people a day, here are the probabilities of meeting at least one psychopath:

p = .04 : .983

p = .01 : .634

p = 1/150 : .488

So, go hug a psychopath … you likely met one today.