# Tree Diagrams

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

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1. In a box there are four red balls and five yellow balls. On Monday Megan 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

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

$$\frac{5}{9}$$

$$\frac{}{}$$

$$\frac{}{}$$

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

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

2. In a round tin there are five cream cakes and six plain cakes. In a square based tin there are five cream cakes and seven 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

$$\frac{5}{11}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

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

3. In a packet there are six lemon sweets and five lime sweets. This morning Megan 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

$$\frac{}{}$$

$$\frac{5}{11}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{}{}$$

$$\frac{4}{10}$$
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? /
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 five red, six blue and seven 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 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

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## Tree Diagrams

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