Probability of Combined Events · 9.3.2
Addition rule of probability
Students confirm, usually by listing outcomes and comparing with the calculated result, that P(A∪B) = P(A) + P(B) for mutually exclusive events, and P(A∪B) = P(A) + P(B) − P(A∩B) for non-mutually exclusive events, understanding why the shared outcomes must only be counted once.
The official learning standard (9.3.2)
“Verify the formula of probability of combined events for mutually exclusive and non-mutually exclusive events.”
What it means
Students confirm, usually by listing outcomes and comparing with the calculated result, that P(A∪B) = P(A) + P(B) for mutually exclusive events, and P(A∪B) = P(A) + P(B) − P(A∩B) for non-mutually exclusive events, understanding why the shared outcomes must only be counted once.
How it is examined
This is mainly explored through classroom activities, so exam focus shifts to applying the verified formula. Paper 1 has short items computing P(A∪B) once the event type is known, while Paper 2 may require showing the reasoning or formula as part of the working before reaching a final probability.
Worked example
In a class of 40 students, 18 like Mathematics (M), 15 like Science (S), and 6 like both subjects. A student is chosen at random.
Verify the formula P(M∪S) = P(M) + P(S) − P(M∩S) by finding P(M∪S) using the formula and by direct counting.
- Direct counting: number of students who like M or S = 18 + 15 − 6 = 27, so P(M∪S) = 27/40.
- Using the formula: P(M) = 18/40, P(S) = 15/40, P(M∩S) = 6/40.
- P(M∪S) = 18/40 + 15/40 − 6/40 = 27/40.
- Both methods give the same result, 27/40, so the formula is verified.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
When do I subtract the intersection?
Only when the events are non-mutually exclusive, meaning they share outcomes. For mutually exclusive events, P(A∩B) = 0, so the formula simplifies to just P(A) + P(B) with nothing subtracted.
What is the general addition rule for probability?
The general rule is P(A∪B) = P(A) + P(B) − P(A∩B). This works for all cases, and it simplifies to P(A) + P(B) automatically when the events are mutually exclusive, since P(A∩B) = 0.
How can I verify the formula without a formula sheet?
List every outcome that belongs to A∪B directly from the sample space and count them to find P(A∪B) by counting. Then compare this with the value calculated using the formula, the two should match.