Did you know? A standard probability cannot be negative. It must lie from 0 to 1 inclusive, or from 0% to 100%. A negative final answer signals that the quantity or the model needs checking.
The important diagnosis is where the work first left that range. A student may have reversed a subtraction, used an impossible input, mixed sample spaces or confused a probability with a signed difference.
Try this now: if P(A) = 0.3, then P(not A) = 1 − 0.3 = 0.7. If a complement calculation gives −0.2, inspect the earlier value and operation; do not simply erase the minus sign.
Choose the task you need
1. Use the valid probability range
Probability measures how likely an event is. Zero represents an impossible event and one represents a certain event, so every standard probability must satisfy 0 ≤ P(event) ≤ 1. As a percentage, that is 0% to 100%.
| Value | Valid probability? | Meaning |
|---|---|---|
| 0 | Yes | The event is impossible in the stated model. |
| 0.35 | Yes | The event has a 35% probability. |
| 1 | Yes | The event is certain in the stated model. |
| −0.2 | No | A negative value cannot be a probability. |
| 1.08 | No | A probability cannot exceed 1. |
Write the range beside the first line of working. It is both a definition and a final reasonableness test.
2. Check fractions and complements
In an equally likely sample space, probability is favourable outcomes divided by total outcomes. Both counts are non-negative, and favourable outcomes cannot outnumber all outcomes, so the fraction stays between zero and one.
Original teaching illustration: if 3 of 10 equally likely cards are blue, P(blue) = 3/10 = 0.3. The complement is P(not blue) = 1 − 0.3 = 0.7. Both values are inside the allowed range and add to one.
If a complement calculation produces −0.2, the subtraction may be arithmetically correct but the input cannot have been a valid probability: 1 − 1.2 = −0.2 exposes the earlier impossible value 1.2.
3. Separate probability from signed quantities
Some calculations legitimately produce negative numbers. A change in temperature, profit, displacement, score difference or correlation can be negative. That does not make the number a probability.
| Quantity | Can it be negative? | Example |
|---|---|---|
| Probability | No | P(rain) = 0.4 |
| Change | Yes | Temperature change = −3°C |
| Net gain or loss | Yes | Profit = −$20 means a loss |
| Signed score | Sometimes | A game rule may award −2 points |
| Probability difference | Yes | P(A) − P(B) can be negative, though neither probability is. |
The label matters. “P(A) = −0.1” is invalid; “P(A) − P(B) = −0.1” can be valid. Ask the student to name the quantity before judging its sign.
4. Diagnose a negative result
When a final probability is negative, work backwards to the first line that left the valid range.
- Label the target. Is the question asking for a probability, a difference or a change?
- Check counts. Favourable and total outcomes cannot be negative, and favourable cannot exceed total in the same sample space.
- Check complements. Subtract a valid event probability from one, not the other way round.
- Check double counting. For unions, subtract the overlap once after adding the two event probabilities.
- Check conditions. Conditional probability uses the size or probability of the stated condition as its new denominator.
This diagnostic route is more useful than replacing a negative sign with a positive one. A sign edit can hide an incorrect model.
5. Transfer the check to harder questions
Experimental probability also remains between zero and one because it is event frequency divided by total trials. Small samples can give unstable estimates, but they cannot justify a negative probability.
Conditional probability and combined-event formulas obey the same boundary. Intermediate expressions may involve subtraction, yet the final probability must return to the 0-to-1 interval. If it does not, inspect the event definitions and overlap before doing more arithmetic.
A strong explanation has three parts: state the range, identify the first invalid step, and correct the model. The same habit used in diagnosis-first secondary mathematics support prevents an impossible answer from becoming a calculator exercise.
Match the help to the student’s actual pathway
Current pathway note, checked 12 October 2026: Posting Groups 1, 2 and 3 support admission to secondary schools; they are not subject levels. Individual secondary subjects may be taken at G1, G2 or G3 according to the student’s programme and the subject available. See MOE’s Full Subject-Based Banding overview.
The Singapore-Cambridge Secondary Education Certificate is introduced from 2027. A relevant syllabus depends on the subject, level, examination year and candidate type; not every subject is offered at every G level. Check the current SEAB SEC information and syllabus list before planning examination support.
For Primary 1–6 and PSLE learners, use the school’s current learning outcomes and the child’s actual work as the starting point. The same diagnosis-first habit can continue through the move to secondary school: identify the precise unstable idea, repair it, then test whether the child can explain and use it independently.
A calm next step for families
A useful tuition conversation starts with evidence: one recent task, what the student attempted, where the reasoning changed, and what the student can explain without prompting. In a verified 3-pax setting, that makes it practical to listen closely, ask a targeted question and give each learner a next task at the right level.
If you would like to discuss diagnosis-first support for probability reasoning and mathematical checking, contact eduKateSG on WhatsApp. The aim is a sensible learning plan, not a grade guarantee.
Sources and checking notes
Concept and policy statements were checked on 12 October 2026. The worked examples and diagnostic prompts in this guide are original teaching illustrations.