Cambridge IGCSE Mathematics · Syllabus 0580 · Probability
Probability of Combined Events
What is Probability of Combined Events?
A combined event involves more than one thing happening, either two features of the same object or two stages of an experiment, and its probability is calculated from a model of all the possible outcomes. Sample-space diagrams and two-way outcome tables list every ordered outcome of a two-part experiment, so that two fair dice give thirty-six equally likely ordered outcomes even though they produce only eleven possible totals, which are not equally likely. Venn diagrams organise overlapping sets and are completed from the intersection outwards, giving the intersection, the only regions, the neither region and the union, all of which must total the universal set; the Core route is limited to two sets while the Extended route is not. In the Extended route the addition rule states that the probability of A union B is the probability of A plus the probability of B minus the probability of A intersection B, so that the overlap is not counted twice, and when the events are mutually exclusive the intersection has probability zero and the rule reduces to simple addition; Core candidates reach the same answers by counting the regions of the diagram. Tree diagrams show successive stages with outcomes written at the ends of the branches and probabilities beside them, probabilities are multiplied along a single complete route and the products of alternative successful routes are added; Core combined events are always with replacement, so the second-stage probabilities are unchanged, while the Extended route also covers sampling without replacement, where both the numerator and the denominator are updated.
This definition is part of the Probability chapter in Cambridge IGCSE Mathematics.