GCSE Maths Practice: two-way-tables

Some probability questions are much more direct than questions involving overlapping groups. In these cases, you are simply asked to find the chance that a randomly selected student has a particular characteristic.

The most important idea in these questions is that probability is always found by comparing two numbers. The top number shows how many outcomes match the description in the question. The bottom number shows how many outcomes are possible in total.

For example, imagine a class where some students enjoy art. If you know how many students enjoy art and you also know the total number of students in the class, you can find the probability by dividing the first number by the second. No extra adjustment is needed because each student is counted only once.

Here is another example. Suppose there are students in a club, and some of them wear glasses. If you want to know the probability that a randomly chosen student wears glasses, you count how many students wear glasses and divide by the total number of students in the club. You do not need to consider boys and girls separately unless the question asks you to.

Sometimes students make mistakes by using the wrong total. For example, they may divide by the number of boys or the number of girls instead of the total number of students. Always check what the question is asking. If it says “a randomly selected student”, the total must include everyone.

Another useful way to think about probability is to imagine picking a name from a hat. Every student’s name is written once and placed into the hat. The probability depends on how many of those names belong to students who fit the description.

Questions like this often appear in GCSE Foundation exams because they test whether students understand the basic probability rule. The key skill is choosing the correct numbers rather than performing difficult calculations.

In real life, this type of probability is used in many situations. Schools might want to know the chance that a randomly chosen student studies a particular subject. Sports teams might look at the chance that a randomly selected player prefers a certain position.

To improve accuracy, always read the question carefully and underline what you are counting and what the total should be. If you can clearly identify these two parts, you are very likely to get the question correct.