Three children with the same birthday?

A recent news story featured a family whose three children had all been born on January 29th. But is this so remarkable?

Let's assume that the birth of a baby in a family is just as likely to occur on any day throughout the year.

The first child can be born on any day, but the chance that the second is born on the same day is 1/365 (ignoring leap years). The chance that the third is born on that day as well is 1/365, and assuming that there is no common factor linking those birthdates then the total chance of the three birthdays coinciding is 1/ (365 x 365 ) = 1 in 133000, or 7.5 in 1,000,000. This is quite small.

But there are 24,000,000 households in Great Britain, and 1,000,000 of them are made up of a couple and 3 or more dependent children [Social Trends 37, page 14, 2007].

Therefore we would expect around 7 or 8 families in Britain to have three children all born on the same day, and so this family is unlikely to be unique in this country. We told this to the journalist from the Times, but it didn't get into the published story.

Following this story, other families reported three siblings all being born on the same day, and two such families were reported last year in the US.

Norman Fenton also covers this story in his excellent Making Sense of Probability site.