A tree diagram can be used to show probabilities of events.
The diagram looks like the branches of a tree.
- The probability of each event should be marked on each branch.
- The probabilities on each set of branches must always add up to 1.
e.g. The tree diagram shows the probabilities when 2 coins are tossed. The coins are "fair" that is there is an equal probability that a "head" or a "tail" will be face up.
From the diagram there are 4 possible outcomes:
Therefore the probability of each of these events occurring is (1 out of 4 possibilities).
This can also be calculated using the multiplication principle. e.g. P(H,H) =
Tree diagrams are useful for dealing with problems of games of chance.
One such game involves picking coloured balls from a bag. There are 8 balls in a bag, 5 of them are red and 3 of them green. If two balls are picked out at random and not replaced, what is the probability of getting two of the same colour?
Draw a tree diagram.
The second selection is out of 7 because one ball has been removed.
From the diagram:
P(Two balls are same colour)
= P(red, red) + P(green, green)