|
|
Tree DiagramsCalculate the probability of independent and dependent combined events using tree diagrams. |
1. In a box there are four red balls and seven yellow balls. On Monday Avery picked a ball at random from the box, played with it then put it back. On Tuesday she picked a ball at random from the box.
a) Complete the tree diagram.
b) What is the probability that on both days she picked a red ball? /
c) What is the probability that on both days she picked a yellow ball? /
d) Calculate the probability that on Monday she picked a red ball and on Tuesday she picked a yellow ball./
Red
Yellow
Red
Yellow
Red
Yellow
2. In a round tin there are five cream cakes and eight plain cakes. In a square based tin there are five cream cakes and nine 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 six lemon sweets and five lime sweets. This morning Avery ate one sweet from the packet before breakfast and she 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 \( \frac{1}{16}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{15}\) otherwise it is \( \frac{1}{14}\) (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 three red, four blue and five 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. |
||
|
|
||
|
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 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary: "I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images. Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?" |
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 ActivitySuko Sujiko Interactive number-based logic puzzles similar to those featuring in daily newspapers designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy. |
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 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 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. | ||
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! |
|
|
||
© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.
https://www.Transum.org/go/?Num=601
Close
Level 1 - Basic probability questions for which the tree diagram has already been drawn
Level 2 - More probability questions requiring you to draw your own tree diagrams
Level 3 - A challenging puzzle that can be solved with the aid of a tree diagram
Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).
More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
Close
