Tree Diagrams

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

ExerciseChallengeExam-Style QuestionsHelpMore Probability

1. In a box there are three red balls and six yellow balls. On Monday Grace 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

$$\frac{3}{9}$$

$$\frac{6}{9}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{3}{9}$$

$$\frac{}{}$$
Monday
Tuesday

2. In a round tin there are four cream cakes and five plain cakes. In a square based tin there are three 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? /
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

$$\frac{4}{9}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$
Round Tin
Square Tin

3. In a packet there are five lemon sweets and eight lime sweets. This morning Grace 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

$$\frac{}{}$$

$$\frac{8}{13}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{7}{12}$$
Before Breakfast
After Breakfast

4. The probability that the first bus is late is $$\frac{1}{18}$$. If the first bus is late, the probability of the second bus being late is $$\frac{1}{17}$$ otherwise it is $$\frac{1}{16}$$ (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

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$
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? /
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

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$
First Counter
Second Counter
Check

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

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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.

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