You and I play a game involving successive throws of a fair coin.
Suppose I pick HH and you pick TH. The coin is thrown repeatedly
until we see either two heads in a row (I win) or a tail followed
by a head (you win). What is the probability that you win?
A gambler bets half the money in his pocket on the toss of a coin,
winning an equal amount for a head and losing his money if the
result is a tail. After 2n plays he has won exactly n times. Has he
more money than he started with?
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand corner
of the grid?
Age 14 to 16 Challenge Level:
Imagine you are in a class of thirty students. The teacher asks
everyone to secretly write down a whole number between 1 and
Do you think it's likely or unlikely that everyone's number will be
You could try this out in your class a few times, or experiment
with this simulation:
How often was everyone's number different?
Are you surprised by this?
Let's try to explain what happens:
Imagine the teacher asks students to read out their numbers one at
What is the probability that the first two students both read out
If the first two students have both read out different numbers,
what is the chance that the third student will read out another new
What is the probability that the first three students all read out
If the first three students have all read out different numbers,
what is the chance that the fourth student will read out another
What is the probability that the first four students all read out
What is the probability that the whole class of thirty students
read out different numbers?
What is the probability that at least two students have
written the same number?
There is a famous mathematical problem called the Birthday
How many people do you need in a room
so that the chance that there
will be at least two people with the
same birthday is greater than 50%?
One way to solve this is to imagine that people enter the room one
at a time, and that each new person doesn't share a birthday with
anyone already there...
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.