GCSE Maths Practice: two-way-tables

When working with probability questions that involve subjects studied at school, it is very common for students to be enrolled in more than one subject. This creates an overlap that must be handled carefully when calculating probabilities.

Imagine a register listing students who take one subject and another register listing students who take a different subject. Some names may appear on both registers. If you simply combine the two lists, those names will appear twice, even though they represent the same student.

In probability, each student must be counted only once when deciding how many students fit a condition. The goal is to find how many students take at least one of the subjects, not how many subject places are filled.

A helpful way to think about this is to focus on people rather than subjects. Ask yourself: “How many individual students are involved?” Anyone who studies both subjects should still only count as one student in the final total.

Some students find it useful to imagine ticking names off a list. First, tick everyone who takes the first subject. Next, tick everyone who takes the second subject. When you reach a name that has already been ticked, you do not tick it again. This ensures no one is counted twice.

After finding the correct number of students who take at least one subject, the probability can be calculated. Probability always compares a favourable group with the total number of possible outcomes. In school survey questions, the total number of outcomes is usually the total number of students.

This type of question is important at GCSE Foundation level because it checks understanding rather than advanced calculation. Examiners want to see that you can interpret information accurately and avoid simple counting errors.

These ideas are also useful outside exams. Schools often analyse subject choices to decide how many classes are needed or how to organise timetables. Counting students correctly ensures fair and efficient planning.

A good habit is to pause before calculating and ask, “Have I counted any student more than once?” This quick check can prevent one of the most common mistakes in probability questions involving two groups.