Probability of A or B when events overlap after PSLE is a useful post-PSLE Mathematics bridge because it connects a familiar idea to the more precise language and reasoning expected in Secondary 1.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. If the same mistake keeps returning, use the Punggol Mathematics diagnostic guide to decide whether the bottleneck is fluency, interpretation, strategy or execution before adding 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 aim is not to rush ahead but to make one important relationship stable enough that later work feels familiar.
WhatsApp eduKatePunggol about a post-PSLE Mathematics transition plan
The short answer: add both event probabilities, then remove the overlap counted twice
If two events can happen together, adding their probabilities directly counts the shared outcomes twice.
The general idea is: P(A or B) = P(A) + P(B) – P(A and B).
The subtraction removes one copy of the overlap so every outcome is counted exactly once.
Start with a simple die example
Roll a fair six-sided die.
Let A = “even” = {2,4,6}. Let B = “greater than 3” = {4,5,6}.
A and B overlap at {4,6}.
Why simple addition overcounts
P(A) = 3/6. P(B) = 3/6.
Adding gives 6/6, but the event A or B actually contains {2,4,5,6}, only four outcomes.
The problem is that 4 and 6 were counted once inside A and again inside B.
Remove one copy of the overlap
P(A and B) = 2/6.
Therefore P(A or B) = 3/6 + 3/6 – 2/6 = 4/6 = 2/3.
When events are mutually exclusive
If A and B share no outcomes, the overlap probability is zero.
Then the rule reduces to simple addition: P(A or B) = P(A) + P(B).
That connects directly to Mutually Exclusive Events After PSLE.
Venn diagrams make the double-counting visible
Imagine two overlapping circles. Adding the size of both circles counts the lens-shaped overlap twice.
Subtracting the overlap once leaves the union counted exactly once.
Worked example: cards numbered 1 to 10
Choose one card from 1 to 10.
A = multiples of 2 = {2,4,6,8,10}. B = multiples of 3 = {3,6,9}.
Overlap A and B = {6}.
P(A or B) = 5/10 + 3/10 – 1/10 = 7/10.
The word ‘or’ usually means inclusive or
In school probability, “A or B” usually includes outcomes in A, in B, or in both unless the context clearly says otherwise.
That is why overlap matters.
A probability-union routine
- Define event A.
- Define event B.
- List or visualise the overlap.
- Find P(A), P(B) and P(A and B).
- Add A and B.
- Subtract one copy of the overlap.
- Check that the final probability lies between 0 and 1.
Independent practice with answers
- On a die, A={2,4,6}, B={5,6}. Find P(A or B).
- Cards 1–12: A=multiples of 2, B=multiples of 4. Find P(A or B).
- If A and B are mutually exclusive with probabilities 0.3 and 0.4, find P(A or B).
- Why is overlap subtracted once?
- Can P(A or B) exceed 1?
Answers: 4/6 = 2/3; 6/12 = 1/2; 0.7; because it was counted twice during addition; no.
How a 3-pax class helps
One student may forget the overlap entirely. Another may subtract it twice. A third may interpret “or” as “only one but not both”.
A small group makes those different meanings visible before formula practice begins.
Frequently asked questions
Why not always just add probabilities?
Because overlapping events share outcomes that would be counted twice.
What if there is no overlap?
Then P(A and B) = 0 and simple addition works.
Why review this after PSLE?
Because it connects probability to sets, Venn diagrams and careful language in a very concrete way.
Continue through the post-PSLE Mathematics route
- After PSLE — Should My Child Start Secondary 1 Maths Early?
- Secondary 1 Math Readiness Checklist After PSLE
- Probability After PSLE
- Mutually Exclusive Events After PSLE
A calm transition is built from precise relationships. Once the student can explain the idea, a fresh question becomes much less intimidating.
