Probability Trees

This lesson can be used for revision for the higher Maths GCSE. The examples are quick and concise with exam style questions, go to GCSE Maths if you need more in-depth explanations.

How to draw probability tree diagrams?

Example 1: There is a bag filled with 2 blue, 8 red and 2 yellow marbles. Deka picks a marble out of the bag, notes its colour and replaces it. She then takes another marble from the bag.
a) Draw a probability tree
b) What is the probability of
(i) getting 2 reds
(ii) getting 2 blues
(iii) getting 2 yellows
(iv) getting 2 different colours

Example 2: There is a bag filled with 2 blue, 8 red and 2 yellow marbles. Deka picks a marble out of the bag, notes its colour and does not replaces it. She then takes another marble from the bag.
a) Draw a probability tree
b) What is the probability of
(i) getting 2 reds
(ii) getting 2 blues
(iii) getting 2 yellows
(iv) getting 2 different colours

Example 3: This probability tree is about Liverpool's chances of winning or not winning their next 2 matches.
The chances for each match are independent.
a) Complete the tree diagram
b) What is the probability of
(i) Liverpool winning both games
(ii) Liverpool losing both games
(iii) Liverpool winning one of the games