GCSE Maths Practice: conditional-probability

Question 1 of 13

This question demonstrates a conditional probability where the condition leaves only one possible outcome.

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\( \begin{array}{l}\text{In a group of 40 people, 24 are male and 16 are female.} \\ \text{If a person is chosen at random, what is the probability that they are female,} \\ \text{given that they are not male?}\end{array} \)

Choose one option:

If the condition removes all other possibilities, the probability is 1.

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 we must ignore them and focus only on what remains.

In this question, the condition is that the selected person is not male. This immediately removes all male people from the group. Once this happens, the only people left in the sample space are females.

A helpful way to think about conditional probability is to imagine physically crossing out outcomes that do not meet the condition. If all males are crossed out, then every remaining outcome is female. Since there are no other possibilities left, the result becomes certain.

This is why the probability is equal to 1. A probability of 1 means the event will definitely occur, given the condition. In contrast, a probability of 0 would mean the event cannot occur under the condition.

For example, imagine a box that contains only red and green counters. If you are told that a counter chosen at random is not green, then it must be red. Given this condition, the probability of choosing a red counter is 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. Under 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 case, dividing by 40 would be incorrect, because the condition has already removed some outcomes. Once the condition is applied, only the remaining outcomes matter.

At Foundation level, questions like this are designed to check whether you understand that conditional probability can sometimes lead to certain outcomes. When the condition removes all alternatives, the probability becomes 1.

To answer conditional probability questions correctly, follow three simple steps. First, identify the condition. Second, remove all outcomes that do not satisfy the condition. Third, calculate the probability using only the remaining outcomes. If only one type of outcome remains, the probability is equal to 1.

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