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Drawing Tree Diagrams

In this lesson, it’ll be necessary to learn to draw tree diagrams to list all the possible outcomes, and to calculate probabilities from this diagram. We’ll begin the lesson by using the example of tossing a coin twice. How many outcomes is possible if a coin is tossed twice?

You might think there are three possibilities, namely two heads, two tails or a head and a tail. But there’s more to the problem than that. We’ll let H be heads and T be tails. What will really help us is a tree diagram. The first part of this tree shows what happens on the first toss of the coin. There are two branches, and we can get either a head or a tail. The next part of the tree shows what happens as a result of the second toss of the coin. Notice that we have four branches — a head, tail, head and tail appear at the end of these four branches.

Now, the good thing about tree diagrams is that by following the paths of the branches left to right we can find all possible outcomes. From the start we can follow the path of the head, which then can lead to a head or a tail in the second set of branches.

Next, from the start we can follow the first branch of the tail to either a head or a tail on the second lot of branches. So, how many outcomes are there and what are they? Well, I hope you can see that there are actually four outcomes, not three. And we can now list them by following the branches in our tree diagram. They are head/head, head/tail, tail/head, and tail/tail. The results head/tail and tail/head might look to be the same but they are different, and have to be counted as separate outcomes.

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