Sum exaggeration

It was with some frustration that I read your story yesterday reporting on the birth of two sets of twins with the same birthday. Whilst I by no means wish to impinge on the happiness of the joyful news for the Sullivan family, I bristled at the mistaken mathematics that would have resulted in the 1 in 30 million odds quoted in the story.

We’re told that Mrs Sullivan has nine children so we can assume she’s had seven successful pregnancies, resulting in two sets of twins and five single births. The chance of a pregnancy resulting in a multiple birth is 1 in 67 . It follows from the binomial distribution that the chances of two out of seven of the pregnancies resulting in multiple birthsis7x6/2x(1/67)^2 x (66 / 67) ^ 5 = 0.43 per cent. We then divide by 365 to give us the probability that the two sets of twins share a birthday, to give us 0.0012 per cent or 1 in 84,116. Long odds, I grant you, but certainly not 1 in 30 million!

GARY THOM Broughton Road, Edinburgh