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
The aim of this activity is for students to acquire a feel for
what a probability distribution is : that it is abstract and though
sample data often follows the theoretical distribution
more closely the larger the sample size it isn't compelled to do
so. It's just a rare event when it doesn't.
Additionally, at Stage 4 students mostly calculate only
individual probabilities and it is helpful to also draw attention
to the profile of probability across the complete range
of values for our variable of interest.
The 'copy to clipboard' facility collects data. Ask students to
collect ten sets of data (ten times 100 throws) pasted
Keep a data set that has the samples separate and another one
which forms a combined sample. These two are to be compared.
Draw the frequency distribution (or relative frequency)
distributions for the first 100, the first 200, then 300 and so
Encourage students into commenting on the graph for
each of these and help them to explain what they observe until this
example of randomness has begun to become secure.
After the samples have been collected and accumulated :