Being Representative

Ms Dickens decides that her English class should practise their debating skills. The motion is to be:

"This class believes it is a good idea for students to learn poems by heart."

But when she asks who wants to speak in the debate, she has far too many volunteers, so she suggests that each side should choose one person to speak for them.

However, Ingrid, says this is unfair.
There are more people on her side than the other, so her chance of being chosen is less than theirs.

There are 4 people who want to speak on behalf of the motion and 12 who want to speak against it, but only time for 2 speakers.

How are the speakers to be chosen?

Ingrid's first suggestion

"Give everyone who wants to speak a number. Then use the random number generator on a calculator to choose two people."

Start by modelling this method.
Put 12 counters (or cubes) in one colour and 4 in another in a non-transparent bag.
Draw out one counter and note which colour it is.
Then put it back and draw out another, noting which colour it is.

How does this model Ingrid's suggestion? Why does the counter need to be put back in the bag? What was the result in your trial?

If you do several trials, do the results appear to model the balance of opinion in the class in a fair way? Does the choice of the second speaker depend on the first at all?

What is the chance of both sides being represented? You should use a tree diagram to help you investigate this.

What are the problems with this model?

Ingrid's second suggestion

"Put the name of everyone who wants to speak in a hat. Then draw out two names."

Model this method.

Put 12 counters (or cubes) in one colour and 4 in another in a non-transparent bag.
Draw out one counter and note which colour it is - do not return it to the bag this time.
Draw out a second counter, noting which colour it is.

How does this model Ingrid's second suggestion? Why is the counter not put back in the bag this time? What was the result in your trial? Does the choice of the second speaker depend on the first at all?

If you do several trials, do the results appear to model the balance of opinion in the class in a fair way?

What is the chance of both sides being represented? You should use a tree diagram to help you investigate this.
How does your tree diagram for this method differ from your first one?

What are the problems with this model?