# Probability Tree Diagrams 1

This applet demonstrates probability tree diagrams, investigating and comparing successive independent events or dependent events, using balls in a bag, with and without replacement.

###### Author and programmer: Ron Barrow

UK Years 9-11, KS3, KS4, Foundation and Higher GCSE Mathematics, Grades C - A* - Data Handling, Statistics and Probability

US - Grades 7 - 10

Instructions below See also: Combining probabilities Tree diagrams 2 Tree diagrams 3 PRINT

## How to Use this Applet

On the screen you will see circles in two colours. These represent the possible outcomes when two balls are drawn randomly from a bag. With this applet you can investigate the probabilities of the different possible outcomes. The number of balls in the bag is given by the two boxes on the left, in the colours of the balls they represent. These numbers can be changed by clicking in the middle the box and then dragging left or right with your mouse. Try it! The probabilities of the the events are drawn as fractions along the branches of the tree diagram. At the end of each branch the probabilities of the successive events (drawing balls from a bag) are calculated. At the bottom further calculations are shown, giving answers to the kinds of questions that these diagrams help to answer. With boxes at the top you can show or hide some of the workings. Checking the "simplify fractions" box will simplify the fractions at the end of calculations. Checking the "further calculations" box will show the working at the bottom. Unchecking the box "branch totals" will hide all the calculations, leaving only the tree and the branch probabilities. One of the important ideas that this applet is designed to investigate is the idea of **independence**. You can examine the different between replacing the balls after each choice, or not replacing them. Use the "with replacement" box to change between the two. Play around! Hopefully you'll quickly gain an insight into this vital topic.