Tree Diagram

Tree diagrams can be a helpful way of organizing outcomes in order to identify probabilities. For example, if we have a box with two red, two green and two white balls in it, and we choose two balls without looking, what is the probability of getting two balls of the same color?

P(same color) = P(RR or GG or WW)

We use the tree diagram to the left to help us identify the possible combinations of outcomes. Here we see that there are nine possible outcomes, listed to the right of the tree diagram. This number is the size of the sample space for this two state experiment, and will be in the denominator of each of our probabilities.

Each of these possible nine outcomes has a probability of 1/9, which we can find using the multiplication rule P(RR or GG or WW) = 3/9.