Shared Ancestors and the Birthday Problem

Lily Agranat-Tamir, Kennedy D. Agwamba, Jazlyn A. Mooney and Noah A. Rosenberg

The American Statistician, 2026, vol. 80, issue 3, 413-422

Abstract: The celebrated birthday problem asks for the probability that in a classroom of k people, there exists at least one pair with a shared birthday; a generalization seeks the probability that in two classrooms of k(1) and k(2) people, at least one shared birthday exists between classrooms. We examine a problem concerning genealogical ancestry as a variant of this ditype birthday problem. Suppose two people descend from the same demographic event. What is the probability that they possess at least one ancestor in common who experienced the event? We use the birthday problem to pose a question concerning genealogies in the African-American population, for which, due to the history of slavery, much genealogical information was not recorded or has been lost: what is the probability that two randomly chosen African-Americans descended from enslaved Africans forcibly transported to North America share at least one such transported ancestor in common? Using a demographic model and the ditype birthday problem, we find that the probability is approximately 19%–31% that two randomly chosen African-Americans born around 1960–1965 possess at least one shared African ancestor. The result contributes to a deeper understanding of African-American genealogies—and it illustrates an application of the birthday problem.

Date: 2026
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DOI: 10.1080/00031305.2025.2595972

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