Probability of Combined Events · Form 4
Probability of Combined Events: Paper 2 Answering Guide
How Probability of Combined Events appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Paper 2 loves a tree diagram: draw it, label the probabilities, then combine them for a compound event. Real contexts, marbles, weather, faulty items, run throughout.
The marks reward a clearly drawn tree as much as the final number.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
The Paper 2 question
A shooter hits a target on any single shot with probability 3/5, and each shot is independent of the others. He fires two shots.
(a) Find the probability that both shots hit. (b) Find the probability that exactly one shot hits.
(c) Find the probability that at least one shot hits.
Mark-earning layout, line by line
- State the complement: P(hit) = 3/5, so P(miss) = 1 − 3/5 = 2/5.
- (a) Multiplication law for independent events: P(hit and hit) = 3/5 × 3/5 = 9/25.
- (b) Exactly one hit has two orders: P(hit, miss) + P(miss, hit) = (3/5 × 2/5) + (2/5 × 3/5).
- Simplify: 6/25 + 6/25 = 12/25.
- (c) At least one hit, using the complement: P(at least one) = 1 − P(miss and miss) = 1 − (2/5 × 2/5).
- Simplify: 1 − 4/25 = 21/25. Check: 9/25 + 12/25 = 21/25, so parts (a)–(c) agree.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I earn marks for the tree diagram itself?
Often yes. A correctly labelled tree usually carries its own mark, and it also sets up the method marks for each product.
Even if your final arithmetic slips, an examiner can see the right method on a clear tree and award the working marks, so always draw and label it fully.
If my final number is wrong but the method is right, do I still score?
In Paper 2 method marks are separate from the answer mark. If you state the correct rule, substitute correctly and only slip in the arithmetic, you keep the method marks and lose just the final accuracy mark.
That is why writing each product like 3/5 × 2/5 before simplifying matters so much.
Should I turn the fractions into decimals for the final answer?
Only if the question asks for a decimal. A fraction like 21/25 is exact and fully acceptable, while a rounded decimal can cost an accuracy mark.
If a decimal is required, keep the fraction through all the working and convert once at the end to avoid rounding errors building up.