2.1. Tree Diagrams http://www.ck12.org
Addition Rule–For 2 events,AandB, the probability of selecting one event or another is given by:P(AorB) =
P(A)+P(B)−P(AandB).
Multiplication Rule–For 2 independent events,AandB, where the outcome ofAdoes not change the probability
ofB, the probability ofAandBis given by:P(AandB) =P(A)×P(B).
Tree diagramsare another way to show the outcomes of simple probability events. In a tree diagram, each outcome
is represented as a branch on a tree.
Example A
If you toss a coin 2 times, what is the probability of getting 2 heads? Use a tree diagram to find your answer.
This is an example of independent events, because the outcome of one event does not affect the outcome of the
second event. What does this mean? Well, when you flip the coin once, you have an equal chance of getting a head
(H) or a tail (T). On the second flip, you also have an equal chance of getting a a head or a tail. In other words,
whether the first flip was heads or tails, the second flip could just as likely be heads as tails. You can represent the
outcomes of these events on a tree diagram.
From the tree diagram, you can see that the probability of getting a head on the first flip is^12. Starting with heads,
the probability of getting a second head will again be^12. But how do we calculate the probability of getting 2 heads?