GCSE Maths Practice: two-way-tables

Question 3 of 10

This question looks at overlapping sports choices.

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\( \begin{array}{l}\textbf{In a group of 100 students, some like football,} \\ \textbf{some like basketball, and some like both.} \\ \textbf{What is the probability that a student likes} \\ \textbf{football or basketball?}\end{array} \)

Choose one option:

Check for overlap before dividing.

When probability questions are based on sports preferences, it is common for students to enjoy more than one sport. This means that the groups of students are not completely separate, and some students belong to both groups at the same time.

The aim of this type of question is to find how many students like at least one of the sports. This includes students who like only one sport as well as those who like both. However, each student should only be counted once in the final total.

A useful way to think about this is to imagine lining students up. First, you include everyone who likes the first sport. Then, you include everyone who likes the second sport. When you come across a student who is already in the line because they like both sports, you do not add them again. This keeps the count accurate.

Some students find it helpful to organise the information into a table. One column can represent students who like one sport, another column for the second sport, and a separate space for students who like both. Organising information visually can reduce mistakes and improve confidence.

After counting the correct number of students who like at least one sport, you can calculate the probability. Probability compares how many outcomes match the condition with how many outcomes are possible in total. In this situation, the total number of possible outcomes is the total number of students.

Questions like this appear often at GCSE Foundation level because they test careful thinking rather than complex calculations. The key skill is recognising that overlapping groups need special attention.

These ideas are useful in everyday life. Sports clubs, schools, and community groups often survey people to see what activities are popular. Correctly counting people who take part in more than one activity helps organisers make better decisions.

To avoid errors in exams, always pause before calculating and ask yourself whether anyone could belong to both groups. If the answer is yes, make sure your method avoids counting those people more than once.

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