What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Winning the Lottery
Age 7 to 11 Challenge Level:
In a far-away land, the lottery consists of four balls numbered $1$
to $4$, which are placed in a bag.
To enter, you choose one number.
To win, your number must match the number that is drawn from the
What is the chance of winning this lottery?
The people running the lottery in this far-away land decide that it
is too easy to win. So, they change their lottery game.
In the new lottery, there are still four balls numbered $1$ to $4$,
which are placed in a bag.
Now, to enter, you choose two numbers.
To win, your numbers must match (in any order) the two numbers that
are drawn from the bag.
What is the chance of winning this new lottery?
Have the organisers made it harder to win compared with their
Can you create your own version of the lottery which would also be
harder to win than the first game?
How do you know that your game is harder?
You may like to use our lottery simulator to try out your
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.