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?
Last One Standing
Age 14 to 16 Challenge Level:
Imagine a school assembly with 250 students. Everyone stands up and
flips a coin. People with tails sit down. People with heads flip
Do you think anyone will get 6 heads in a row?
How many heads in a row do you expect the last one standing to have
Can you explain your reasoning?
Here is an animation for you to explore what happens when different
sizes of assembly gather and carry out the experiment.
Now that you have had the chance to explore, do your answers
and reasoning to the questions above change at all?
What is the probability of flipping ten heads in a row?
How many people would you need to have in a school assembly for you
to expect there to be someone still standing after ten flips?
Here are some related questions you might like to consider:
The probability of winning the lottery jackpot if you buy one
ticket is approximately 1 in 14 million.
There are usually two jackpot winners every week. How many tickets
do you think are sold each week?
On October 7th 2010, a woman gave birth to her third child. Her
first two children were also born on October 7th, in 2005 and 2007.
So all three children in the family have the same birthday. The
odds of this happening were incorrectly reported in the newspapers
as being 1 in 48 million. Can you work out the correct
There are more than a million families in the UK with three
Would you expect there to be other families with three children who
share a birthday?
The television performer Derren Brown once filmed himself
flipping ten heads in a row for a programme about horse racing and
unlikely events. He used a fair coin, and kept filming until he got
ten in a row. How long do you think it took him?
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.