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Tree Diagrams

Calculate the probability of independent and dependent combined events using tree diagrams.

Exercise Challenge Exam-Style Questions Help More Probability

1. In a box there are three red balls and six yellow balls. On Monday Antonio 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? /CorrectWrong
c) What is the probability that on both days he picked a yellow ball? /CorrectWrong
d) Calculate the probability that on Monday he picked a red ball and on Tuesday he picked a yellow ball./CorrectWrong

Red

Yellow

Red

Yellow

Red

Yellow


\( \frac{3}{9} \)
CorrectWrong

\( \frac{6}{9} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{3}{9} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong
Monday
Tuesday

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

Cream

Plain

Cream

Plain

Cream

Plain


\( \frac{4}{9} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong
Round Tin
Square Tin

3. In a packet there are five lemon sweets and eight lime sweets. This morning Antonio 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? /CorrectWrong
c) What is the probability of picking a lemon sweet followed by a lime sweet? /CorrectWrong
d) Calculate the probability of picking a lime sweet followed by a lemon sweet?./CorrectWrong

Lemon

Lime

Lemon

Lime

Lemon

Lime


\( \frac{}{} \)
CorrectWrong

\( \frac{8}{13} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{7}{12} \)
CorrectWrong
Before Breakfast
After Breakfast

4. The probability that the first bus is late is \( \frac{1}{17}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{16}\) otherwise it is \( \frac{1}{15}\) (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? /CorrectWrong
c) What is the probability of both buses being on time? /CorrectWrong
d) What is the probability of at least one bus being on time? /CorrectWrong

Late

On Time

Late

On Time

Late

On Time


\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong
First Bus
Second Bus

5. In a bag there are four red, five blue and six 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? /CorrectWrong
c) What is the probability of both counters not being red? /CorrectWrong
d) What is the probability of at least one counter being red? /CorrectWrong

Red

Not red

Red

Not red

Red

Not red


\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong

\( \frac{}{} \)
CorrectWrong
First Counter
Second Counter
Check

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.

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Featured Activity

Lemon Law

Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

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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:

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Apple

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Description of Levels

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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 exam-style questions involving tree diagrams

Tree Diagrams

This video explains how to use tree diagrams to solve probability questions and is from Corbettmaths.

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.

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