GCSE Maths Practice: conditional-probability

Conditional probability is used when we are asked to find the probability of an event under a specific condition. The condition tells us that some outcomes are no longer possible, so the sample space becomes smaller.

In this question, the condition is that the selected student is not female. This immediately removes all female students from consideration. Once this happens, the only students left in the sample space are male students.

A useful way to think about conditional probability is to imagine physically removing outcomes that do not meet the condition. If we cross out all female students, we are left only with males. Since every remaining outcome is male, the probability of selecting a male from this restricted group is certain.

This type of question is often used at Foundation level to test whether students understand that some conditional probabilities can be equal to 1 or 0. A probability of 1 means the event will definitely happen under the given condition, while a probability of 0 means it cannot happen.

For example, suppose a box contains only red and blue balls. If you are told that a ball chosen at random is not red, then it must be blue. In this situation, the probability that the ball is blue given that it is not red is equal to 1.

Another example involves days of the week. If you are told that today is not a weekday, then it must be a weekend day. Given this condition, the probability that today is Saturday or Sunday is 1.

Students sometimes make the mistake of still using the original total number of outcomes when answering conditional probability questions. In this question, using 25 as the denominator would be incorrect because the condition has already removed some outcomes. Once the condition is applied, only the remaining outcomes matter.

It is important to remember that conditional probability always works within the restricted group defined by the condition. You should ask yourself: “What outcomes are still possible now?” and ignore everything else.

To summarise, conditional probability follows three simple steps. First, identify the condition. Second, remove any outcomes that do not meet the condition. Third, calculate the probability using only the remaining outcomes. When the condition leaves only one possible outcome, the probability is equal to 1.