Thursday, 20 November 2014

The Absent Sibling Question

Will you believe this? It's counter-intuitive.

In the 1911 census for England and Wales there's information on how long a marriage has lasted, how many children there have been and how many are still alive. That's in addition to information on names, ages, relationships, etc.

Suppose you have a family where the couple has been married for 25 years, they had two child who are both still alive and one of them, a girl age 21, is living at home.

Is the other child more likely to be male or female?

What do you think?

If a couple have two children the possibilities, in birth order, are:


Assume that each possibility is equally likely even though boy births occur slightly more frequently than girl births.

In this case knowing one of them is a girl we can eliminate the Boy-Boy possibility. That leaves three options two of which pair a girl with a boy and one with a girl.

It's twice as likely the other sibling not at home with the parents is a boy rather than a girl.

If you knew the girl at home was the elder, or the younger, there would be an equal chance the absent child would be male of female.



turner said...

No, I'm not surprised.
It would be unusual if a couple married 25 years in 1911 with one 21 year old at home would not have had a child prior to that one. It's highly likely that the one not at home would have been a boy.
But, oh, John, must you? Cheers,

Chad Milliner said...

But the 1911 census does not say anything about birth order. Therefore, girl-boy and boy-girl are really the same thing, and so they should not be counted twice. Hence, there is not twice as much chance of the other child being male.

JDR said...

The reasoning does not depend on the 1911 census census specifying birth order.