Let us start by assigning variable a to be the probability the
pregnant women is under 40 years of age, since the number of weeks of
pregnancy is only 40.
Our expression for the probability is "a".
Now assuming that there is no calendar variation in birth rates (any
day of the year has roughly the same number of birthdays as any other
number - which may fail 9 months from Valentine's day), then there is
a 40 week / 52 week chance that the women's birthday falls during the
Our probability expression is now (40/52)a.
Next, the woman's birthday must fall on the same day of week as the
conception. That's one in seven:
Our probability expression is now (40/52)(1/7)a.
Interpreting things so far, we know the woman is turning an age under
40 during the pregnancy and her birthday is on some whole number of
weeks from conception. Since there are 40 possible "whole number of
weeks" and she has a birthday on just one of those, we apply a 1/40
Our probability is now (40/52)(1/7)(1/40)a.
That should give us the likelihood you are looking for. If we make
the estimate that 95% of pregnancies are to mothers under age 40, then
a=.95 and so our calculation would make the probability:
P = (40/52)(1/7)(1/40)(.95) = 0.0026 (with rounding)
or about a 1 in 400 chance.
Stephen La Rocque.>