Probability of Combined Events
Sample space
The set of all possible outcomes of an experiment, written S.
| English | Sample space |
|---|---|
| Bahasa Melayu | Ruang sampel |
| 中文 | 样本空间 |
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
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.