Drawing a Tree Diagram
A
tree diagram shows all the possible outcomes of an event and their
probabilities.
For example, we can draw the tree diagram of a single coin toss.
How to Draw a Tree Diagram
A single coin toss can be drawn on a tree diagram.
Draw a single coin toss on a tree diagram.
StepbyStep:
1
List the possible outcomes of the event.
If a coin is tossed, the coin can land on
Heads or
Tails.
2
Draw a branch for each outcome of the event. Label each outcome.
3
Find the probability of each outcome and write it by the the branch.

The probability of Heads is ^{1}⁄_{2}. It is written by the branch.

The probability of Tails is ^{1}⁄_{2}. It is written by the branch.
Answer:
We have drawn the tree diagram that represents the single tossing of a coin.
How to Draw a Tree Diagram with More Than One Event
A tree diagram can be drawn for more than one event.
A coin can be tossed twice, one time after another. This can be drawn on a tree diagram.
Draw a double coin toss on a tree diagram.
1^{st} Toss
Consider the first toss of the coin.
The tree diagram for the first toss will be the same as the tree diagram for a single toss.
2^{nd} Toss
Consider the second toss of the coin.
We extend the tree diagram to the right.
For each branch of the 1
^{st} toss, we can draw another 2 branches, showing the same two outcomes.
1^{st} Toss Was Heads
Another tree diagram can be drawn from the
Heads branch of the
1^{st} toss.
1^{st} Toss Was Tails
Another tree diagram can be drawn from the
Tails branch of the
1^{st} toss.
Lesson Slides
The above example was simple because the tossing of a coin is an
independent event. The probability of getting
Head or
Tails is always the same.
Drawing a tree diagram for a
dependent event is more complicated. The slider below another real example of how to draw a tree diagram.