Chapter 10: Brainteasers 367
constraints
−√
(1−ρXY^2 )(1−ρYZ^2 )+ρXYρYZ≤ρXZ≤√
(1−ρXY^2 )(1−ρYZ^2 )+ρXYρYZ.For this particular example we have 0. 4585 ≤ρXZ≤
0 .9815. It is interesting how small the correlation can be,
less than one half, considering how high the other two
correlations are. Of course, if one of the two correla-
tions is exactly one then this forces the third correlation
to be the same as the other.
Airforce One
One hundred people are in line to board Airforce One.
There are exactly 100 seats on the plane. Each passen-
ger has a ticket. Each ticket assigns the passenger to a
specific seat. The passengers board the aircraft one at a
time. GW is the first to board the plane. He cannot read,
and does not know which seat is his, so he picks a seat
at random and pretends that it is his proper seat.
The remaining passengers board the plane one at a
time. If one of them finds their assigned seat empty,
they will sit in it. If they find that their seat is already
taken, they will pick a seat at random. This continues
until everyone has boarded the plane and taken a seat.
What is the probability that the last person to board
the plane sits in their proper seat?
(Thanks to Wilbur.)
Solution
Sounds really complicated, because of all the people
who could have sat in the last person’s seat before