Replies

First off, note that this event is no more or less likely than the four births occurring on any other specified combination of dates. So, while amazing because of the coincidence, it's really not that big a deal statistically.

Now to the numbers:

1. Assuming that impregnation is equally probable on any given month; and assuming normal variations in gestation time, one can reasonably assume that any given birthday on a given year is equally likely. (P=1/365.25)

2. Assume that impregnation is equally likely in any given year over the ~20 child-bearing years of the mother.

3. So the probability of having a birthday on any given day over that 20 years is 1/(365.25*20) = 1/7305.

4. Assuming that the births are statistically independent (perhaps not a good assumption), the probability of ANY four births occurring on specified dates is (1/7305)⁴ = ~1/3¹⁵.

Note again that any specified combination of 4 birthdays is equally likely (or unlikely).