So far, we have looked at using tree diagrams to find the outcomes of multiple events when we are given the probability of a single event.

Now we need to look at doing this the other way round.

Example 1: A bag contains red and blue balls. A ball is picked out, the colour noted and then replaced. This is repeated.

If the probability of picking out two red balls is 1/25. What is the probability of picking out two blue balls.

Step 1: Lets put this into a tree diagram.

**Step 2: What can we work out?**

We know that the probabilities are the same for each event because we are told the ball is replaces.

If we know that P_{(AA)} = 1/25, this is the same as saying P_{(A)} x P_{(A) }= 1.25 so P_{(A)} = 1/5

**Step 3: Work out the other event.**

We know that A and B are exhaustive, so P_{(B)} must equal 4/5

**Step 4: Complete the rest of the tree diagram.**

**Step 5: Use this to answer the question.**

We were intially asked for the Probability of 2 blue balls. From the tree diagram, we can now see that this is 16/25