Sample space tables after PSLE is a useful post-PSLE Mathematics bridge because it makes one familiar idea more precise before Secondary 1 adds faster symbolic work.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. If a mistake keeps repeating, the Punggol Mathematics diagnostic guide helps separate fluency, interpretation, strategy and execution before simply assigning more practice.
At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT. The small format makes the student’s setup and explanation visible, so the tutor can repair the first weak step rather than only the last answer.
WhatsApp eduKatePunggol about a post-PSLE Mathematics transition plan
The short answer: organise all possible outcomes before counting favourable ones
Probability becomes unreliable when students count from memory and accidentally miss or repeat outcomes.
A sample space table gives every combination one place, making the denominator visible before the probability is calculated.
Start with two coins
Toss two coins. The possible ordered outcomes are HH, HT, TH and TT.
There are four equally likely outcomes in the usual fair-coin model.
The probability of exactly one head is 2/4 = 1/2 because HT and TH both qualify.
Why HT and TH are different outcomes
HT means first toss heads, second toss tails. TH means first toss tails, second toss heads.
The final count of heads is the same, but the ordered outcomes are different.
Build a 2 × 2 table
Put H and T across the top for the first coin and H and T down the side for the second coin. The four cells become HH, HT, TH and TT.
The table makes it difficult to omit a combination.
Worked example: coin and die
A fair coin and a fair six-sided die are used together.
There are 2 × 6 = 12 equally likely ordered outcomes: H1 through H6 and T1 through T6.
If the event is “heads and an even number”, the favourable outcomes are H2, H4 and H6, so probability = 3/12 = 1/4.
The denominator comes from the whole sample space
Students sometimes count three favourable outcomes and divide by six because the die has six faces. But the combined experiment has twelve possible outcomes.
The sample-space table protects the denominator by showing the full experiment.
Worked example: two number spinners
Spinner A has 1, 2 and 3. Spinner B has 1 and 2. Assume all sectors are equally likely.
There are 3 × 2 = 6 outcomes.
For a sum of 4, the favourable ordered pairs are (2,2) and (3,1), so probability = 2/6 = 1/3.
Tables help when the condition is verbal
A condition such as “at least one tail”, “sum greater than 4” or “same number on both spinners” can be checked cell by cell.
This reduces the chance that a keyword is interpreted too quickly.
A sample space can connect to sets
The whole table is the sample space. An event is a subset of those outcomes.
This gives a natural bridge to Sets and Venn Diagrams After PSLE.
A complement can be faster
With two fair coins, the event “at least one head” contains HH, HT and TH.
The only outcome with no heads is TT, so P(at least one head) = 1 – 1/4 = 3/4.
That connects to Probability Complements After PSLE.
A sample-space routine
- Identify each stage or object.
- List possible outcomes for each.
- Build rows and columns systematically.
- Count total outcomes.
- Mark favourable outcomes.
- Divide favourable by total when 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.
How a 3-pax class helps
One student may omit outcomes. Another may double-count them. A third may build the table correctly but misread the event condition.
The tutor can see whether the bottleneck is enumeration, language or fraction calculation.
Frequently asked questions
Do I always need a sample space table?
No. Use it when it makes combined outcomes clearer. Very simple experiments may be listed directly.
Are all cells automatically equally likely?
Only if the underlying outcomes are equally likely and the table is built from those equally likely choices.
Why review this after PSLE?
Because Secondary probability becomes easier when the sample space is organised before any probability formula is used.
Continue through the Post-PSLE to Secondary 1 Mathematics route
- After PSLE — Should My Child Start Secondary 1 Maths Early?
- Secondary 1 Math Readiness Checklist After PSLE
- Probability After PSLE
- Probability Complements After PSLE
Mathematics Tuition in Punggol: make the representation trustworthy
Secondary Mathematics becomes easier when the child can move between words, diagrams, numbers and symbols without changing the meaning.
That is the real value of a careful post-PSLE bridge.
