Shaking A Six

Shaking A Six	Statistics In Your World

Student Notes

Teachers Notes

Making Biased Dice

Do Biased Dice Help You Win?

AnotherExperiment

Is There Any Difference

Unfair Dice
Ordinary dice are fair. Every number has the same chance of coming up at each throw. We call this UNBIASED. Some dice are unbalanced. For example, six may come up more often than it should. When this happens we say the die is BIASED in favour of six.

Making Biased Dice
You will need:
A piece of thin card or paper (9 cm by 7 cm), some sellotape.

On the piece of card draw six squares like this. Make the side of each square 2 cm long.

Figure 3 - Net for a die

Number the squares as in the diagram.

On the back of either square 1 or square 6 sellotape or glue some extra card. Make a note of which number you choose. If you have sellotaped extra card to square 1, your die is biased in favour of a six. If the extra card is sellotaped to square 6, your die is biased in favour of a one.

Why?

Cut out the shape and fold the squares to make a cube. Either stick the tabs with glue or use sellotape to make the cube firm.

Notice that one and six are on opposite faces of the die. A die biased in favour of six is biased against one. A die biased in favour of one is biased against six.

Do not tell the pair working with you where you have stuck the extra card.

Do Biased Dice Help You Win?
Imagine vou repeated the experiment to throw a six with a die biased in favour of six.

a	Would it be easier or harder to get a six?
b	Would it take more throws or fewer throws to get a six?
c	How would the shape of Figure 1 change?
d	Do you expect the median for the biased die to be higher, lower, the same?

Another Experiment
You will need:
Squared paper, Table 4 on page R2.

Work in pairs. Exchange biased dice with the other pair. Your die is biased in favourof either a one or a six. Try, to throw a six with your biased die. It may not roll easily. Spin it in the air like tossing a coin

a	Repeat the experiment in Section Al using this die. Throw until you have scored 25 sixes. Record the results in Table 4.
b	Draw a bar chart of your results.
c	Find the mode of the number of throws.
d	Find the median of the number of throws.

Is There Any Difference?
Compare your new bar chart with Figure 1, Throwing a six.

	a	Does the shape of the new bar chart differ from Figure 1? Why is this?
	b	Has the mode changed using the biased die? Is it higher, lower, the same?
	c	Has the median changed using the biased die? Is it higher, lower, the same?
	d	Is the die you are using biased in favour of or against six? Give a reason. Ask the other pair if you are correct.
*	e	Could we play Ludo with a die biased in favour of a six? What differences would it make?

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