Probability of Combined Events
Mutually exclusive events
Events that cannot both happen at the same time.
| English | Mutually exclusive events |
|---|---|
| Bahasa Melayu | Peristiwa saling eksklusif |
| 中文 | 互斥事件 |
How it is used
Rolling a fair die, getting a '2' and getting a '5' are mutually exclusive. P(2 or 5) = P(2) + P(5) = 1/6 + 1/6 = 2/6 = 1/3, since the two outcomes never overlap.
Where it shows up in SPM
Used in the addition rule for combined events, P(A or B) = P(A) + P(B) when A and B cannot both happen. It links to sets, as mutually exclusive events have an empty intersection.
Paper 1 tests the quick rule; Paper 2 embeds it in structured questions with dice, cards or coloured balls.
Don't confuse it with
Open the chapter: Probability of Combined Events →
Frequently asked questions
How do I recognise mutually exclusive events?
Ask whether both events could be true in a single trial. If a die shows one face at a time, '2' and '5' cannot both occur, so they are mutually exclusive.
If they can overlap, like 'even' and 'greater than 3' which share the value 4, they are not.
Why can't I just always add probabilities when I see 'or'?
Simple addition only works when events are mutually exclusive. If they can overlap, adding double-counts the shared outcomes, so the full rule is P(A or B) = P(A) + P(B) − P(A and B).
At SPM level most 'or' questions are set up to be mutually exclusive, so check first.