Cambridge IGCSE Mathematics · Syllabus 0580 · Probability
Conditional Probability
What is Conditional Probability?
A conditional probability is the probability of one event calculated on the understanding that another event is already known to have happened. It is found by restricting the model to the part in which the given condition holds and then treating that part as the whole: on a two-way table the row or column total named by the condition becomes the new denominator, on a Venn diagram the region named by the condition becomes the new universal set, and on a tree diagram the second-stage branch probabilities after a particular first-stage outcome are already conditional probabilities. When a condition covers several routes of a tree, the probabilities of the routes that satisfy the condition are added and the probability of the wanted routes is expressed as a share of that total. The result is generally different from the unconditional probability, and it is not symmetrical: the probability of A given B and the probability of B given A are usually different numbers. Knowledge of the notation P of A given B, and of formulas relating to conditional probability, is not required by the syllabus, so every calculation is carried out directly from the table, diagram or tree.
This definition is part of the Probability chapter in Cambridge IGCSE Mathematics.
Examiner tips on Conditional Probability
- The one boundary worth memorising. If a question makes you take something out and not put it back, it is an Extended question. Every without-replacement tree, every changing denominator and every conditional probability in this chapter sits inside an Extended block for exactly that reason.