Probability
Probability measures chance from 0 to 1. For equally likely outcomes, divide favourable outcomes by all possible outcomes. For successive events, track what changes after each step, especially when objects are not replaced.
What this guide covers
Single and combined events, possibility and tree diagrams, mutually exclusive events and independent events. Count equally likely outcomes only when that assumption is justified.
Syllabus reference: 2026 Mathematics 4052, S2, page 11. These are Mentora search groupings, not new official syllabus categories.
Worked example
A bag contains 3 red and 2 blue counters. Two are drawn at random without replacement. Find the probability both are red.
The first red has probability 3/5. After it is removed, 2 red counters remain among 4 counters, so the second red has probability 2/4. Multiply along this path: (3/5)(2/4) = 3/10.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
A fair six-sided die is rolled. Find the probability of a number greater than 4.
Show worked answer
The favourable outcomes are 5 and 6, so probability = 2/6 = 1/3.
Check 2
P(A) = 0.37. Find P(not A).
Show worked answer
An event and its complement cover all outcomes, so P(not A) = 1 − 0.37 = 0.63.
Check 3
Two fair coins are tossed independently. Find the probability of exactly one head.
Show worked answer
The equally likely outcomes are HH, HT, TH and TT. Exactly one head occurs in HT and TH, so probability = 2/4 = 1/2.
Common mistakes to watch for
- Without replacement, both the numerator and denominator can change on the next draw.
- Mutually exclusive means events cannot happen together; independent means one does not change the probability of the other.
- Add disjoint paths and multiply successive conditional probabilities along a path. Do not assume independence just because two events are named separately.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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More G3 Math topicsPublished by Mentora · Sources checked 11 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.