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?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two bags
so as to make the probability of choosing a red ball as small as
possible and what will the probability be in that case?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
Stage: 4 Challenge Level:
The key idea in all this is to see how a probability
distribution gives a theoretical description of the random
situation, but that this does not mean that our sample data must
You will also see how larger samples often get closer to the
theoretical distribution but that the sample is not compelled to
behave like that (it's random after all), although it's
a rare event when it doesn't.
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. More information on many of our other activities
can be found here.