Probability of lots of twins

Dave Radcliffe asked on Twitter: “A class of 380 students has 16 sets of twins. How likely is this to happen purely by chance?” and he links to this article. The school in question is the Staples High School in Westport, Connecticut.

Let’s assume for the sake of argument that if there are two twins, they will be in the same grade at the same school. Then we may as well treat each pair of twins as a single person for the purpose of school-enrollment purposes, and so we’re asking: out of 364 entities which are either singletons or pairs of twins, what’s the probability of at least 16 twins?

This refers to the class of 2014 at this school, so let’s figure they were born in 1996. This data brief from the CDC gives the rate of twin births in 1996 at about 27 per 1000. But that’s counted per-child. If you count per-pregnancy you should get just over half that; let’s call it 14 per 1000. The probability that a binomial(364, 0.014) random variable is at least 16 is about one in 14,000.

(The data brief, however, points out one interesting fact – Connecticut has the highest rate of twinning. Different states have quite different rates of twinning, which appear to be explained at least partially by different distributions of age and race of mothers giving birth.)

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