Probability of Combined Events · 9.3.1
Mutually exclusive events
Students learn that mutually exclusive events cannot occur at the same time and share no common outcomes, such as rolling a 2 or a 5 on one die. Non-mutually exclusive events share at least one common outcome, such as drawing a card that is red or a king.
This distinction decides which addition rule to use later.
The official learning standard (9.3.1)
“Differentiate between mutually exclusive and non-mutually exclusive events.”
What it means
Students learn that mutually exclusive events cannot occur at the same time and share no common outcomes, such as rolling a 2 or a 5 on one die. Non-mutually exclusive events share at least one common outcome, such as drawing a card that is red or a king.
This distinction decides which addition rule to use later.
How it is examined
Paper 1 usually presents two events based on dice, cards or spinners and asks students to identify whether they are mutually exclusive, sometimes using a Venn diagram. Paper 2 may require this distinction as a step within a larger combined-events question, justified using set notation such as A∩B = ∅.
Worked example
A fair die is rolled once. Event A: getting an even number.
Event B: getting a number greater than 4. Determine whether A and B are mutually exclusive.
- List the outcomes: A = {2, 4, 6} and B = {5, 6}.
- Find the intersection: A∩B = {6}.
- Since A∩B ≠ ∅ (not empty), the two events share the outcome 6.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What does mutually exclusive mean in simple terms?
It means two events cannot happen at the same time in a single trial, they have no outcomes in common. For example, a die showing an odd number and a die showing a 6 cannot both happen on one roll.
How can I check quickly during the exam?
List the outcomes of each event as sets and compare them. If no value appears in both lists, the events are mutually exclusive; if at least one value appears in both, they are non-mutually exclusive.
Can you give an example of non-mutually exclusive events?
Drawing a card that is a heart, and drawing a card that is a queen, are non-mutually exclusive, the queen of hearts satisfies both events, so their outcome sets overlap.