Probability of Combined Events

Mutually exclusive events

Events that cannot both happen at the same time.

EnglishMutually exclusive events
Bahasa MelayuPeristiwa 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

Independent eventsMutually exclusive events cannot happen together so we add their probabilities, while independent events can happen together and we multiply.
Complementary eventComplementary events are a special mutually exclusive pair that also covers every outcome, so their probabilities add to exactly 1, whereas general mutually exclusive events need not.

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.

Related terms

One-hour paid trial · Same-day replyfrom RM50/hr
Book a Trial Class