360 Frequently Asked Questions In Quantitative Finance
that ‘shot’ it becomes fifty-fifty and if you are successful
four times in a row then the next shot will definitely
be fatal.
Matching birthdays
You are in a room full of people, and you ask them all
when their birthday is. How many people must there be
for there to be a greater than 50% chance that at least
two will share the same birthday?
(Thanks to baghead.)
Solution
This is a classic, simple probability question that is
designed to show how poor is most people’s perception
of odds.
As with many of these type of questions it is easier to
ask what are the chances of two peoplenothaving the
same birthday. So suppose that there are just the two
people in the room, what are the chances of them not
having the same birthday? There are 364 days out of 365
days that the second person could have, so the proba-
bility is 364/365. If there are three people in the room
the second must have a birthday on one of 364 out of
365, and the third must have one of the remaining 363
out of 365. So the probability is then 364× 363 / 3652.
And so on. If there arenpeople in the room the proba-
bility of no two sharing a birthday is
364!
(365−n)!365n−^1
.
So the question becomes, what is the smallestnfor
which this is less than one half? And the answer to this
is 23.
