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 DiagramQuestion: 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 DiagramThe 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 1st toss is represented by the same tree diagram as above.
The 2nd toss is drawn in a similar way. But it is drawn to the right of the 1st 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 DiagramThe 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.
NoteWHAT 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 DIAGRAMSTree diagrams can be any size.
It would be possible to draw a tree diagram for three coin tosses:
A USEFUL CHECKThere 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