Sample space tables after PSLE help students list every combined outcome before counting favourable cases. This makes probability more systematic and reduces missed or duplicated outcomes.
The wider transition guide is After PSLE — Should My Child Start Secondary 1 Maths Early?. At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT.
The short answer: organise the whole sample space before calculating probability
If two fair coins are tossed, the ordered outcomes are HH, HT, TH and TT. Exactly one head occurs in HT and TH, so the probability is 2/4 = 1/2.
Why HT and TH both matter
HT means the first toss is heads and the second is tails. TH reverses that order. They have the same number of heads but are different ordered outcomes.
Build a table to protect the denominator
Put the possible outcomes of one stage across the top and the outcomes of the second stage down the side. Each cell then represents one combined outcome.
Worked example: coin and die
A fair coin and fair six-sided die give 2 × 6 = 12 ordered outcomes. “Heads and an even number” gives H2, H4 and H6, so the probability is 3/12 = 1/4.
Dividing by 6 would ignore the coin. The sample space makes the full denominator visible.
Worked example: two spinners
Spinner A has 1, 2 and 3. Spinner B has 1 and 2. There are six ordered outcomes.
A sum of 4 occurs at (2,2) and (3,1), so the probability is 2/6 = 1/3.
Sample spaces connect to sets
The whole table is the sample space. An event is a subset of those outcomes. This connects naturally to Sets and Venn Diagrams After PSLE.
Complements can make counting faster
With two fair coins, “at least one head” is the complement of TT. So the probability is 1 – 1/4 = 3/4.
Read Probability Complements After PSLE for the wider shortcut.
A sample-space routine
- Identify each stage or object.
- List the possible outcomes for each.
- Build rows and columns systematically.
- Count the total outcomes.
- Mark the favourable outcomes.
- Divide favourable by total when the outcomes are equally likely.
- Check the result lies between 0 and 1.
Independent practice with answers
- Two coins are tossed. Find P(two heads).
- Two coins are tossed. Find P(at least one tail).
- A coin and die are used. Find P(tails and a number greater than 4).
- Spinner A has 1,2,3 and Spinner B has 1,2. Find P(sum = 3).
Answers: 1/4; 3/4; 1/6; 1/3.
Frequently asked questions
Are all cells automatically equally likely?
Only when the underlying choices are equally likely.
Why review this after PSLE?
Because Secondary probability becomes much easier when the sample space is organised before any formula is used.
Return to the post-PSLE Mathematics hub or WhatsApp eduKatePunggol.
