So far, we have looked at using tree diagrams to find the outcome 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: Let's 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 that the ball is replaced.

If we know that P_{(RR)} = 1/25, this is the same as saying P_{(R)} x P_{(R) }= 1/25 so P_{(R)} = 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 initially asked for the probability of two blue balls. From the tree diagram, we can now see that this is **16/25**

Let's move on to some questions now.