# How to Draw a Tree Diagram (Mathematics Lesson)

# What Is a Tree Diagram?

A tree diagram displays the possible outcomes from an event, and allows the probabilities of different outcomes to be calculated.# How to Draw a Tree Diagram

**Question:**Draw a tree diagram for the tossing of a coin:

**Step 1:**List the possible outcomes of the event.

The possible outcomes of tossing a coin are the coin coming up

**Heads**or

**Tails**.

**Step 2:**Draw a branch for each outcome of the event, being sure to label it.

**Step 3:**For each outcome, find the probability, and write it by the relevant branch.

The probability of getting a

**Head**is

**½**, and the probability of getting a

**Tail**is also

**½.**

This is the tree diagram that represents the tossing of a coin.

# A Real Example of How to Draw a Tree Diagram

The above example showed a tree diagram for a single event.It is possible to draw a tree diagram for several, sequential events.

For example, imagine tossing a coin twice, one time after the other.

The 1

^{st}toss is represented by the same tree diagram as above.

The 2

^{nd}toss is drawn in a similar way. But it is drawn to the right of the 1

^{st}toss. It must also be drawn for each of the outcomes of the previous toss:

This is the tree diagram that represents two tosses of a coin.

# Another Real Example of How to Draw a Tree Diagram

The above example was relatively simple because the tossing of a coin is an independent event. The probability of getting a**Head**or

**Tail**is always the same.

Drawing a tree diagram for a dependent event is more complicated.

The slider below gives a real example of how to draw a tree diagram for sequential dependent events.

##### Interactive Test

**show**

##### Note

**WHAT IS PROBABILITY?**

Probability tells us how likely something is to happen.

The probability of an event is defined as:

Probability is given as a number between 0 and 1.

A probability of 0 means an event is impossible.

A probability of 1 means an event is certain.

The closer a probability is to 0 the less likely it is. The closer a probability is to 1 the more likely it is.

# SIZE OF TREE DIAGRAMS

Tree diagrams can be any size.It would be possible to draw a tree diagram for three coin tosses:

##### Top Tip

# A USEFUL CHECK

There is a useful way to check that the probabilities on a tree diagram are all right.Notice that at each branch, the probabilities add up to 1:

Read more about adding fractions