Probability of Combined Events
Complementary event
The event that A does not happen; its probability is 1 − P(A).
| English | Complementary event |
|---|---|
| Bahasa Melayu | Peristiwa pelengkap |
| 中文 | 互补事件 |
How it is used
If P(rain tomorrow) = 0.3, the complementary event is 'no rain', with probability P(no rain) = 1 − 0.3 = 0.7. The two must add to 1.
Where it shows up in SPM
A powerful shortcut in combined-events questions, especially for 'at least one' problems where finding P(none) first and subtracting from 1 is far quicker. It appears in both papers, and links to the complement of a set, A′, from the Sets topic.
Don't confuse it with
Open the chapter: Probability of Combined Events →
Frequently asked questions
When should I use the complement instead of adding cases directly?
Use it whenever an event has many favourable cases but its opposite has few. 'At least one' is the classic signal: instead of adding one, two, three… successes, compute 1 − P(none).
For example P(at least one head in 3 tosses) = 1 − (1/2)³ = 7/8.
Is the complement of an event the same as its negation in logic?
They are the same idea in different topics. In probability the complement of event A is 'A does not happen', with P(A′) = 1 − P(A).
In logic, negation reverses a statement's truth value. Both describe the opposite, but only the probability version has the 1 − P(A) relationship.