# 296. Jellybean Trees

How on earth can you create a maths lesson using these items?

Well, first sort them into colours, then put twenty jelly beans into each cup. Make sure there are only two colours in each cup, write the contents on a sticky label and use that to seal the cup. Each cup should have slightly different numbers or colours – it prevents copying.

Note: Eat all the orange jelly beans – you’ll be doing your dignity a favour!

Have you figured it out yet? No? We’re doing probability tree diagrams without replacement. Now I know you could do this with one experiment at the front of the class, but getting everyone involved means it’s more hands-on and memorable.

The Experiment
I did a demonstration of this on the board first, before handing out the cups and worksheets. I told the class what was in my cup and picked out a jellybean. It was orange. I drew the first stage of the worksheet (see below) on the board: What was the experiment? How many of each colour do we have? What is the probability of each colour? Then we filled in the first stage of the tree diagram.

I ate the jellybean.

But you can’t do that – it messes up the experiment! I asked what would be the probabilities for a second jellybean now. They figured out the slight change to the probabilities. Then we went back and thought about what would have happened if my first jellybean had been lemon.

I always encourage students to work out all the possible outcomes before they even look at the rest of the questions. And this is why you need to eat all the orange – the list on the board was:

• P(LL) =
• P(LO) =
• P(OL) =

Do I really need to put the last one?

After much giggling, the class were let loose with their own cups. They did the experiment once with their standard cups and then had their work checked. They could then alter (eat) the contents of their cup so that a minimum of five beans of two colours remained. You can see an example of a student’s work here:

I summarised the lesson by looking at different types of probability problem where items are not replaced. I now have a nice ‘hook’ to refer to when discussing probability tree diagrams without replacement.

Tree diagram without replacement (pdf)
I printed out two per page as it fitted nicely in their books. The descriptions are deliberately vague to allow it to be used in different experiments.

(The usual warning regarding food allergies and beliefs stands. Some jellybeans have animal derivative gelatine – please check, you don’t want to accidentally upset a student)

# 14. JDs Tree Diagram

My friend JD came up with this visual way of explaining tree diagrams. I’m reproducing it here with permission (Thanks!). It helps if you have a school uniform with a tie and jumper, however this could easily be done with coats and hats.

Set Up
You need 6 volunteers, dressed as listed:
1. (No jumper, no tie) x 2
2. (No jumper, tie) x 2
3. Jumper, tie
4. Jumper, no tie

(This can be adapted for listing multiple outcomes too)

Activity
Draw a V shape on the ground.
Explain that in the morning you have choices when you get dressed. Each branch represents a choice.
Choice 1: Do you put your tie on or not?
Get a student wearing a tie to stand at the end of one branch and one without a tie to stand at the end of the other

Draw a V from each student.
Choice 2: Do you put your jumper on or not?
Get the class to decide who stands where

Discussion
If all the choices are equally likely, what is the probability of getting in trouble with your teacher over uniform?
Can you prove this by looking at the probabilities of the individual events?
What would happen if the outcomes were not equally likely?

It’s a good idea to try and take a picture of what this looks like to display in class. You could also annotate it with fractions and overall probabilities.