Shaking A Six Statistics In Your World 
Student Notes
Teachers Notes
Even or Odd?
 
Charting Sixes
 

The Probability of a Six

How, often are you likely to throw a six?
Do you think it is about once in every 2 throws,
once in every 4 throws,
once in every 6 throws,
once in every 8 throws,
something else?

Write down which statement you think is true. Give a reason for your answer.

Even or Odd?
You will need:
Page R5. an ordinary die, a coloured pen or pencil.

You will later use a chart to find out how often a six is likely, to show up.

Here is a different experiment to show how the chart works.

Throw a die. An even number is a success, an odd number is a failure. Use Figure 7 on page R5.

Here are the rules:

Put your pencil on the point marked Start. Throw the die. If the number is even (a success), mark the path down to the next point on the right.

If the number is odd (a failure), mark the path down to the next point on the left. Keep throwing and continue the path until you reach the bottom of the chart. This will be after 20 throws of the die.

David did his experiment. He threw:
4,2,3,1,5,4,1,3,3,6,4,3,6,5,2,4,5,6,5, 1,
His path is shown in Figure 2.

Figure 2 - Trowing a die - David's results

a Follow his path to see how it is plotted.

In Figure 2 the numbers at the left are the numbers of throws. The number of points in from the left tells you how many successes you have had. This can also be written as a fraction or a decimal.
b How many successes did David have after 20 throws?
What fraction was this?
c How many successes did David have after 10 throws?
What fraction was this?
d Do the experiment with your own die. Plot your path in Figure 7 on page R5.
e How many successes did you have after 20 throws?
What fraction is this?
f How many successes did you have after 10 throws?
What fraction is this?

Get a friend's results.
g Use these to continue your path for 40 throws in
Figure 8 on page R5.

Turn Figure 8 so that the Number of throws axis is at the bottom.
Look again at the path you have drawn.
h Does the line seem to settle down?
i At about what level?
j Is this what you expected? Give a reason.

Eventually the line settles down near a particular fraction. This fraction is called the PROBABILITY Of throwing an even number with your die.

Charting Sixes
You will need:
Page R4, an ordinary die, a coloured pen or pencil.

Work in pairs. One person throws the die while the other plots the route.

Figure 9 on page R4 is like Figure 8 but can record 100 throws. This time you are trying to throw a six. Throw the die 100 times. Plot the route on Figure 9 as you did on Figure 8. Move to the right for a success (i.e. throwing a six) and to the left for a failure (i.e. throwing a one, two, three,four or five).

The dotted lines show the proportion of sixes. '2 in 6' means two sixes thrown for every six throws of the die.

a How many successes did you have from 100 throws?
What fraction was this?

Turn Figure 9 so that the Number of throws axis is at the bottom.

Look again at the path you have drawn.
b Does the line seem to settle down?
c At what level?
d Is this what you expected? Give a reason.

The fraction at this settling-down level is the probability of throwing a six with your die.

 

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