Solution. We will use R to mean taking a red stick, W to mean taking a white stick and B to mean taking a blue stick

We will use R to mean taking a red stick, W to mean taking a white stick and B to mean taking a blue stick. The tree diagram is shown below.

The probability of taking a certain colour of stick is written on the appropriate branch.

By multiplying the probabilities along one branch we find the probability of one outcome. Hence there are nine possible outcomes. If we add all the probabilities of the outcomes together, the answer will be 1.

a) We need the branch marked *.

P(RR) means the probability of taking a red stick and then taking another red stick.

b) We need the branch marked .

c) The order in which we take the blue stick and the white stick does not matter. Thus we require the probability of taking a blue stick followed by a white stick and the probability of taking a white stick followed by a blue stick. Hence we use two separate branches and then add the answers. The two branches required are marked and O.

d) We could add all the branches that contain an event B. Since we know the total probability is 1, it is actually easier to subtract the probabilities of those branches that do not contain an event B from 1. These are marked.

NOTE! We can also use tree diagrams to help us with conditional probability.