GCSE Maths Practice: two-way-tables

Probability questions that involve preferences or choices often include overlapping groups. This means that some people may belong to more than one group at the same time. In this type of problem, it is important to count people carefully so that each person is only included once.

If you add the number of people in each group without checking for overlap, the total will usually be too large. This happens because people who belong to both groups are included twice. These students should only be counted once when finding how many people are included overall.

A useful way to understand this is by imagining a simple diagram with two circles. One circle represents people who like the first option, and the other circle represents people who like the second option. Where the circles overlap shows people who like both. This overlap helps you see which people have been counted more than once.

Another helpful strategy is to work step by step. First, count everyone who likes the first option. Then include everyone who likes the second option. Finally, adjust your total so that anyone who appears in both groups is only counted once. This approach reduces mistakes and keeps your working clear.

After finding the correct number of people who fit the description, the probability can be calculated. Probability compares the number of favourable outcomes with the total number of possible outcomes. In class-based questions, the total number of outcomes is usually the total number of students.

Many students find these questions challenging because they rush or overlook the overlap. Taking a moment to identify whether the groups share members can prevent simple errors. Examiners expect this awareness at Foundation level.

These questions are common in GCSE Maths because they relate to everyday situations, such as sports choices, clubs, or survey results. Learning to organise information carefully is a useful skill beyond exams.

As a final tip, always read the question slowly and look for words like “both”, “either”, or “or”. These words tell you how the groups connect and guide you toward the correct method.