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
Here is an example of something called a 'probability
What is the probability for no sixes, or for one six only, or
two sixes, three, four, or all five?
To understand more about distributions look at the Distribution Maker environment below.
Hold down SHIFT while you click audio
for a commentary to help you make sense of what you are looking at.
Holding down SHIFT opens the audio in a separate window; minimise
that window to see this page again.
The audio commentary talks about two other distributions:
rolling one die, and the sum of two dice, before discussing the
Five Dice context above, and will help you see that a probability
distribution is a profile of how the probability varies as the
variable we are interested in (for example the numbers of sixes
seen each time) ranges randomly across its set of possible
Use the distribution maker to throw a
single die 100 times. Do this two or three times. Why isn't the
graph of actual values a horizontal line like the yellow
Now use the 'copy to clipboard'
facility and paste the values to something like a spreadsheet. The
'Copy to Clipboard' button puts the data to the Windows clipboard.
If, for example in Excel or Word, you then
click on Paste, the data will appear.
If you do that ten times you will
have data for 1000 throws. You should be able to sort those in the
spreadsheet which will make counting the frequency much easier (in
Excel for example, get all the data into one column, select the
column and then use Sort
from the Data menu)
How many of the samples of 100 are
less even (horizontal or rectangular) than the combined sample of
When you have grasped the connection
between a sample and the abstract probability distribution (the
conditions under which that sample has been drawn) you are ready
Matching as a natural next challenge.