GCSE Maths Practice: tree-diagrams

This question is a Higher-tier tree diagram problem because it requires students to think carefully about the structure of the experiment, not just the numerical probabilities. Although the spinner itself does not change between spins, the key difficulty lies in deciding how to represent the situation correctly using a tree diagram.

The spinner is divided equally into six numbered sections, so the probability of landing on any given number on a single spin is 1/6. This applies to both spins because the spinner is unchanged. However, Higher GCSE questions often test whether students understand when a tree diagram is still useful even for independent events.

The first stage of the tree diagram represents the outcome of the first spin. One branch corresponds to landing on 4, and the other branch represents landing on a number other than 4. Only the branch where the spinner lands on 4 is relevant to the question, because the second spin is only of interest in that case.

On the branch where the first spin is 4, the spinner is spun again. The second stage of the tree diagram shows the possible outcomes of this second spin, including landing on 2 or not landing on 2. Each of these outcomes has a probability of 1/6 and 5/6 respectively.

A common mistake at this level is to ignore the structure of the experiment and immediately multiply 1/6 by 1/6 without showing any working. While this may give the correct numerical answer, it does not demonstrate the reasoning expected in Higher GCSE questions, especially when tree diagrams are specifically mentioned.

Tree diagrams help organise thinking by showing each stage of the experiment clearly. They make it obvious which outcomes are possible, which branches should be followed, and which branches are irrelevant. This is particularly useful in more complex Higher questions, where some branches may stop early or where multiple paths must be added together.

For example, if the question asked for the probability of landing on a 4 and a 2 in any order, two different paths would need to be considered: 4 then 2, and 2 then 4. A tree diagram makes it easy to identify and calculate both paths before adding them together.

In summary, although the probabilities in this question are simple, the Higher-level skill lies in recognising how to represent the experiment accurately using a tree diagram and in clearly identifying the correct path needed to answer the question.