Apply Algebra to Tree Diagrams

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.