Probability of Combined Events · 9.3.3
Probability of A or B
Students calculate P(A or B) using either the listing method, writing out the sample space and counting favourable outcomes, or the addition rule formula, choosing P(A) + P(B) for mutually exclusive events or P(A) + P(B) − P(A∩B) when outcomes overlap.
The official learning standard (9.3.3)
“Determine the probability of combined events for mutually exclusive and non-mutually exclusive events. Determination of the probability of combined events need to involve: (i) Listing of the outcomes of events based on representation, or (ii) Using the formula”
What it means
Students calculate P(A or B) using either the listing method, writing out the sample space and counting favourable outcomes, or the addition rule formula, choosing P(A) + P(B) for mutually exclusive events or P(A) + P(B) − P(A∩B) when outcomes overlap.
How it is examined
Paper 1 features short questions giving two events involving dice, coins or cards and asking for P(A or B), testing quick and accurate formula application. Paper 2 often embeds this within multi-part questions using tables or Venn diagrams, requiring students to identify any overlap before computing the final probability with full working.
Worked example
A card is drawn at random from a set of cards numbered 1 to 20. Event A: the number is a multiple of 3.
Event B: the number is a multiple of 5. Find P(A or B).
- List A = {3, 6, 9, 12, 15, 18}, so n(A) = 6.
- List B = {5, 10, 15, 20}, so n(B) = 4.
- Find the intersection: A∩B = {15}, so n(A∩B) = 1 (non-mutually exclusive, since 15 is a multiple of both 3 and 5).
- P(A) = 6/20, P(B) = 4/20, P(A∩B) = 1/20.
- P(A or B) = 6/20 + 4/20 − 1/20 = 9/20.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do I always subtract the intersection?
Only when the events are non-mutually exclusive and share outcomes. For mutually exclusive events, the intersection is empty (P(A∩B) = 0), so the formula becomes simply P(A) + P(B).
Can I just list outcomes instead of using the formula?
Yes, listing every outcome in A∪B directly from the sample space is an accepted method and gives the same answer. It's also a good way to double-check your formula-based working in the exam.
How do I know if two events in a question are mutually exclusive?
List the outcomes of each event and check whether they share any value. If A∩B is empty, the events are mutually exclusive; if they share at least one outcome, they are non-mutually exclusive.