GCSE Maths Practice: tree-diagrams

This is a Higher-tier tree diagram question because the second spin does not automatically happen after every first spin. Instead, the experiment depends on the outcome of the first spin, and only certain branches of the tree continue. Understanding when a branch should continue and when it should stop is a key Higher GCSE skill.

The spinner has four equal sections: Red, Blue, Green and Yellow. Each colour has the same probability of occurring on a single spin, which is 1/4. The first stage of the tree diagram therefore shows four equally likely outcomes.

The important detail in this question is that the spinner is spun a second time only if the first spin is Red. This means that the tree diagram must stop on all other branches (Blue, Green and Yellow). A common mistake is to extend every branch to a second spin, which would incorrectly suggest that the second spin always happens.

On the Red branch, the spinner is spun again. Because the spinner is unchanged, the probabilities on the second spin are the same as on the first: each colour has probability 1/4. This makes the second stage independent of the first, but only along the Red branch.

To find the probability of Red followed by Blue, we identify the correct path on the tree diagram: Red → Blue. Probabilities along a single path are multiplied together. Even though the events themselves are independent, the structure of the experiment still requires a tree diagram to show which outcomes are possible.

Higher GCSE tree diagram questions often combine simple probability values with more complex structure. The difficulty does not always come from the fractions themselves, but from deciding which branches of the tree are valid and which should stop. This is why drawing a clear tree diagram is strongly recommended.

For comparison, consider a similar situation where the spinner is always spun twice. In that case, all branches would continue and the problem would usually be Foundation tier. By adding a condition that controls whether the second spin happens, the problem becomes more challenging and requires careful interpretation of the experiment.

When answering exam questions like this, always read the description carefully and ask yourself: does every outcome lead to the next stage? If not, your tree diagram must reflect that.