Tree DiagramsCalculate the probability of independent and dependent combined events using tree diagrams. 
1. In a box there are five red balls and six yellow balls. On Monday James picked a ball at random from the box, played with it then put it back. On Tuesday he picked a ball at random from the box.
a) Complete the tree diagram.
b) What is the probability that on both days he picked a red ball? ^{}/_{}
c) What is the probability that on both days he picked a yellow ball? ^{}/_{}
d) Calculate the probability that on Monday he picked a red ball and on Tuesday he picked a yellow ball.^{}/_{}
Red
Yellow
Red
Yellow
Red
Yellow
2. In a round tin there are six cream cakes and seven plain cakes. In a square based tin there are three cream cakes and eight plain cakes. The tree diagram shows the probabilities of picking one cake from each tin.
a) Complete the tree diagram.
b) What is the probability of picking two cream cakes? ^{}/_{}
c) What is the probability of picking two plain cakes? ^{}/_{}
d) Calculate the probability of picking two different types of cake.^{}/_{}
Cream
Plain
Cream
Plain
Cream
Plain
3. In a packet there are seven lemon sweets and six lime sweets. This morning James ate one sweet from the packet before breakfast and he ate another after breakfast. Both sweets were picked randomly from what was in the packet at the time.
a) Complete the tree diagram.
b) What is the probability of picking two lemon sweets? ^{}/_{}
c) What is the probability of picking a lemon sweet followed by a lime sweet? ^{}/_{}
d) Calculate the probability of picking a lime sweet followed by a lemon sweet?.^{}/_{}
Lemon
Lime
Lemon
Lime
Lemon
Lime
4. The probability that the first bus is late is \( \frac{1}{14}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{13}\) otherwise it is \( \frac{1}{12}\) (buses are either on time or late, they are never early!).
a) Complete the tree diagram.
b) What is the probability of both buses being late? ^{}/_{}
c) What is the probability of both buses being on time? ^{}/_{}
d) What is the probability of at least one bus being on time? ^{}/_{}
Late
On Time
Late
On Time
Late
On Time
5. In a bag there are six red, seven blue and eight green counters. Two counters are taken out and not replaced.
a) Complete the tree diagram.
b) What is the probability of both counters being red? ^{}/_{}
c) What is the probability of both counters not being red? ^{}/_{}
d) What is the probability of at least one counter being red? ^{}/_{}
Red
Not red
Red
Not red
Red
Not red
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 



Transum.orgThis web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available. Please contact me if you have any suggestions or questions. 
More Activities: 

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex: "This website was brilliant. My class and I really enjoy doing the activites." Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." 


AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy adfree access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe 

Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic. TeachersIf you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows: 

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. 
© Transum Mathematics :: This activity can be found online at:
www.transum.org/Maths/Activity/Tree_Diagrams/Default.asp?Level=1
Close
Level 1  Basic Tree Diagram questions
Level 2  A challenging puzzle that can be solved with the aid of a tree diagram
Level 3  GCSE and IB examstyle questions involving tree diagrams
This video explains how to use tree diagrams to solve probability questions and is from Corbettmaths.
Close