GCSE Maths Practice: two-way-tables

Question 7 of 10

This question involves subject choices and overlap.

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\( \begin{array}{l}\textbf{In a group of 70 students, some study science,} \\ \textbf{some study arts, and some study both.} \\ \textbf{What is the probability that a student studies} \\ \textbf{science or arts?}\end{array} \)

Choose one option:

Check carefully for students counted in both subjects.

Probability questions that involve school subjects often describe students choosing more than one option. This means that the groups in the question can overlap. Some students may study both subjects, while others study only one.

The goal in this type of question is to find the chance that a randomly selected student studies at least one of the subjects mentioned. This includes students who study only science, students who study only arts, and students who study both.

A helpful way to think about this is to imagine a timetable. Some students appear on the science timetable, some appear on the arts timetable, and some appear on both. Even if a student appears on two timetables, they are still just one student and should only be counted once.

One strategy is to think about counting students one by one. Start by counting all students who study science. Then include students who study arts. When you reach a student who already studies science and arts, do not add them again. This keeps the total accurate.

Another way to organise the information is to use a simple table with three sections: students who study only science, students who study only arts, and students who study both. This structure helps you clearly see where overlap occurs.

Once the correct number of students who study at least one subject has been found, the probability can be calculated. Probability compares the number of favourable outcomes with the number of possible outcomes. In this situation, the possible outcomes are all students in the group.

Questions like this are common at GCSE Foundation level because they test attention to detail rather than difficult calculations. Many errors happen when students rush and forget to account for overlap.

These skills are useful beyond exams. Schools use similar calculations when planning subject options, staffing, or classroom space. Counting students correctly helps ensure that resources are allocated fairly.

A good final check before answering is to ask yourself whether any student could have been counted more than once. If the answer is yes, make sure your method corrects for that before finding the probability.

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