Probability of Combined Events · 9.1.1
Combined events in probability
Students learn that a combined event is formed by joining two or more events with 'and' or 'or', then systematically list every possible outcome that makes up that combined event, using tools such as tables, tree diagrams, or organised lists, without yet calculating any probability.
The official learning standard (9.1.1)
“Describe combined events and list out the possible combined events.”
What it means
Students learn that a combined event is formed by joining two or more events with 'and' or 'or', then systematically list every possible outcome that makes up that combined event, using tools such as tables, tree diagrams, or organised lists, without yet calculating any probability.
How it is examined
This standard mainly builds the foundation for later probability topics. Paper 1 may ask students to identify or describe a combined event from a scenario, while Paper 2 often requires listing outcomes of a combined event as the first step before calculating its probability in a later part.
Worked example
A fair die is rolled and a fair coin is tossed together. List all the possible outcomes of the combined event 'the die shows an even number and the coin shows Head'.
- List the die's possible outcomes: 1, 2, 3, 4, 5, 6. The even numbers among these are 2, 4 and 6.
- List the coin's possible outcomes: Head (H) and Tail (T).
- The combined event requires the die to show an even number AND the coin to show Head, so pair each even die outcome with H.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What exactly is a combined event?
A combined event is an event formed by joining two or more events together, usually using the word 'and' or 'or'. For example, 'rolling an even number and tossing a Head' combines a die event with a coin event into a single event.
What's the easiest way to list combined events without missing any outcomes?
Use a two-way table or a tree diagram and work through it in a fixed order, such as listing every outcome of the first event before pairing each one with every outcome of the second event.
Is a combined event the same as an intersection of two sets?
Not always, a combined event using 'and' corresponds to an intersection, while one using 'or' corresponds to a union. This standard only asks you to describe and list outcomes; calculating probability comes in a later standard.