GCSE Maths Practice: two-way-tables

In probability questions involving drinks or preferences, it is very common for people to choose more than one option. This means that the groups described in the question are not completely separate. Some students may appear in both groups at the same time.

The aim of this type of question is to find the chance that a randomly chosen student drinks at least one of the drinks mentioned. This includes students who drink only one of the drinks as well as students who drink both.

One way to think about this situation is to imagine a list of students. First, you list everyone who drinks the first drink. Then, you add everyone who drinks the second drink. As you add names, you may notice that some names already appear on the list because those students drink both. When this happens, you should not add the name again.

This idea is important because probability is about counting people, not counting choices. A student who drinks both coffee and tea is still just one student, so they must only be counted once in the final total.

Here is a different example to help explain the idea. Imagine a group of people where some own a phone and some own a tablet. Some people own both devices. If you want to know the probability that a randomly chosen person owns a phone or a tablet, you must be careful not to count people with both devices twice.

Once you have correctly counted how many students drink at least one of the drinks, finding the probability is straightforward. The probability is found by comparing that number with the total number of students. The total number of students represents all possible outcomes.

Questions like this often appear in GCSE Foundation exams because they test careful reading and logical thinking. Many mistakes happen when students rush and forget to check for overlap between groups.

These ideas are also useful in real life. For example, a school might use survey results to decide what drinks to offer at an event. Counting students correctly helps avoid buying too much or too little.

A good exam habit is to 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.