Tree Diagrams

Menu Level 1 Level 2 Level 3 Exam Help More

1. In a box there are two red balls and five yellow balls. On Monday Landon 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? / Correct Wrong
c) What is the probability that on both days he picked a yellow ball? / Correct Wrong
d) Calculate the probability that on Monday he picked a red ball and on Tuesday he picked a yellow ball./ Correct Wrong

Red

Yellow

Red

Yellow

Red

Yellow

\( \frac{2}{7} \)

\( \frac{5}{7} \)

\( \frac{}{} \)

\( \frac{2}{7} \)

\( \frac{}{} \)

Monday

Tuesday

2. In a round tin there are three cream cakes and four plain cakes. In a square based tin there are four cream cakes and five 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? / Correct Wrong
c) What is the probability of picking two plain cakes? / Correct Wrong
d) Calculate the probability of picking two different types of cake./ Correct Wrong

Cream

Plain

Cream

Plain

Cream

Plain

\( \frac{3}{7} \)

\( \frac{}{} \)

Round Tin

Square Tin

3. In a packet there are four lemon sweets and three lime sweets. This morning Landon 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? / Correct Wrong
c) What is the probability of picking a lemon sweet followed by a lime sweet? / Correct Wrong
d) Calculate the probability of picking a lime sweet followed by a lemon sweet?./ Correct Wrong

Lemon

Lime

Lemon

Lime

Lemon

Lime

\( \frac{}{} \)

\( \frac{3}{7} \)

\( \frac{}{} \)

\( \frac{2}{6} \)

Before Breakfast

After Breakfast

4. The probability that the first bus is late is \( \frac{1}{12}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{11}\) otherwise it is \( \frac{1}{10}\) (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? / Correct Wrong
c) What is the probability of both buses being on time? / Correct Wrong
d) What is the probability of at least one bus being on time? / Correct Wrong

Late

On Time

Late

On Time

Late

On Time

\( \frac{}{} \)

First Bus

Second Bus

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? / Correct Wrong
c) What is the probability of both counters not being red? / Correct Wrong
d) What is the probability of at least one counter being red? / Correct Wrong

Red

Not red

Red

Not red

Red

Not red

\( \frac{}{} \)

First Counter

Second Counter

This is Tree Diagrams level 1. You can also try:
Level 2 Level 3

Instructions Try 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.

	You are learning this because future ideas are built on previous ideas and the more ideas you learn the more power you have to learn anything, ever! The world's best football player engages in rigorous training, practicing skills repeatedly to prepare for the big game. While the specific actions rehearsed during these exercises are rarely needed in the match, the very process of performing these drills enhances their overall prowess as a top player. more...	More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
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 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich: "My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."		Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity ChristMaths Christmas activities make those December Maths lessons interesting, exciting and relevant. If students have access to computers there are some online activities to keep them engaged such as Christmas Ornaments and Christmas Light Up.	Answers There 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 ad-free 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 Maths Learning 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 Map Are 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.
Teachers
If 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:	Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.	It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!
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.