Probability of Combined Events

Sample space

The set of all possible outcomes of an experiment, written S.

EnglishSample space
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How it is used

When two fair coins are tossed, the sample space is S = {HH, HT, TH, TT}, giving n(S) = 4 equally likely outcomes. So P(exactly one head) = 2/4 = 1/2.

Where it shows up in SPM

The starting point for almost every probability question. In Paper 2 you often list the sample space as a set, a two-way table, or an ordered-pair grid before counting favourable outcomes.

Getting n(S) right is essential because it is the denominator of every probability that follows.

Don't confuse it with

EventThe sample space is the set of all possible outcomes, while an event is a subset of it, such as 'getting at least one head'.
Universal setThey play the same role, but 'universal set' is the term in the Sets topic while 'sample space' is its name in probability, both being the full collection under consideration.

Open the chapter: Probability of Combined Events →

Frequently asked questions

What is the difference between the sample space and n(S)?

The sample space S is the actual list of outcomes, like {HH, HT, TH, TT}. The symbol n(S) is just how many outcomes are in that list, here 4.

You list S to make sure you count correctly, then use n(S) as the denominator in your probability.

Do I have to list every outcome, or can I just count them?

For small problems listing is safest and earns clear method marks. For larger ones a two-way table or the multiplication principle is quicker, for example two dice give 6 × 6 = 36 outcomes.

List when you can, and count systematically so you neither miss nor repeat an outcome.

Related terms

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