Chapter 10: Brainteasers 381
certain assumptions about the distribution of the sexes
of offspring among couples. Consider a population in
which each couple can only ever have boys or only
ever have girls. Those who have boys could stop after
one child, whereas those who have girls can never stop
having children, with the end result being more girls
than boys. (Of course, this might not matter since
the goal is for there to be more males, there is no
requirement on the number of females.) And if there
is any autocorrelation between births this will also have
an impact. If autocorrelation is one, so that a male child
is always followed by a male, and a female by a female,
then the ratio of males to females decreases, but with a
negative correlation the ratio increases.
Aircraft armour
Where should you reinforce the armour on bombers?
You can’t put it everywhere because it will make the
aircraft too heavy. Suppose you have data for every hit
on planes returning from their missions, how should
you use this information in deciding where to place the
armour reinforcement?
(Thanks to Aaron.)
Solution
The trick here is that we only have data for aircraft that
survived. Since hits on aircraft are going to be fairly
uniformly distributed over all places that are accessible
by gunfire one should place the reinforcements at pre-
cisely those places which appeared to be unharmed in
the returning aircraft. They are the places where hits
would be ‘fatal.’ This is a true Second World War story
about the statistician Abraham Wald who was asked
precisely this.