Author: Ton Lecluse

Probability tree

 Introduction The construction box Plane geometry Investigating a section Investigating a function Drawing in perspective A probability tree The calculator Getting a taste Downloads Register Back to start

This exercise requires you to set the difficulty level to high (in the configuration window). Geocadabra offers a few nice applications when it comes to probability. This demo allows for a limited probability tree to be drawn.

We are about to solve the following problem.

A vase is filled with 2 red and 8 blue balls.
After you have paid  1,25 you are allowed to pick two balls in one go. Eyes closed of course!You get paid  3,- for every red ball and nothing for every blue ball you pick. Do you expect your chances of winning to increase or decrease depending on the number of turns?

Analysis of the model.

What we are dealing with is a draw without replacement from a vase containing 2 red and 8 blue balls.

A probability tree will help us list all possible draws in one chart. By processing this probability tree and by determining the expected value of the turn out you get an impression of whether you will get paid more or less than your original stake.

 A computation using Geocadabra. We will start by selecting a new drawing. Choose statistical methods, probability tree and press [OK]. A probability tree box appears in which we can now select the data we want to use.

Mind the details:

The sampling type should be without
replacement

Name of knot points: numerical.
After all, we wish to calculate using
amounts.
Depth: 2;
We will take 2 balls from the vase
Split count per knot: 2.
You can either pick a blue or a red
ball so there are 2 possibilities per
ball
Process knot points: sum;
Every red ball is linked to  3,- and
every blue ball to  0,- and it is
these amounts you wish to
calculate with.
Numerical information at each
branch: probability (as a fraction)
Starting values of each type:
2 (red) and 8 (blue).
Value of each type:  3,- for the red ball and  0,- for the blue ball
You can click on the red or the blue square to select a colour. In this example the colours have already
been set.

Now click the [process] button. The tree is drawn.

Sometimes the texts in the graph right from the tree are off screen. Click the buttons where it says tree measurements to adjust the size of the tree horizontally or vertically.

The tree will look like below:

If you were to, for example, follow the top branch you would get the following information:The probability of getting two red balls equals . The sum of the total turnout ( 3,- per red ball) equals  6,-.