368 Frequently Asked Questions In Quantitative Finance
their turn. Start by considering just two people, GW and
you. If GW sits in his own seat, which he will do 50%
of the time, then you are certain to get your allocated
seat. But if he sits in your seat, again with 50% chance,
then you are certain to not get the right seat. Soapriori
result, 50% chance. Now if there are three people, GW
either sits in his own seat or in your seat or in the
other person’s seat. The chances of him sitting in his
own seat or your seat are the same, and in the former
case you are certain to get your correct seat and in
the latter you are certain to not get it. So those two
balance out. If he sits in the other person’s seat then
it all hinges on whether the other person then sits in
GW’s seat or yours. Both equally likely, end result 50-50
again. You can build on this by induction to get to the
simple result that it is 50-50 whether or not you sit in
your allocated seat.
Hit-and-run taxi
There was a hit-and-run incident involving a taxi in a
city in which 85% of the taxis are green and the remain-
ing 15% are blue. There was a witness to the crime who
says that the hit-and-run taxi was blue. Unfortunately
this witness is only correct 80% of the time. What is the
probability that it was indeed a blue car that hit our
victim?
(Thanks to orangeman44.)
Solution
A classic probability question that has important conse-
quences for the legal and medical professions.
Suppose that we have 100 such incidents. In 85 of these
the taxi will have been green and 15 blue, just based
on random selection of taxi colour. In the cases where
