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.
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.
Useful foundations to check
These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.
Basic probability and single events
List single-event outcomes before building a two-step sample space or tree.
Practise probabilityPerform the four basic arithmetic operations: addition, subtraction, multiplication, and division on whole numbers, fractions, and decimals.
Count favourable and total outcomes carefully, then simplify their fraction. Two favourable out of six gives 1/3.
Practise probability
Applications and next topics
Use tree diagrams for multi-step choices and compare predicted probabilities with observed data. Statistics describes the observations; finite observed frequencies can differ from theoretical probabilities.
Choose a useful next resource
To understand a recurring error rather than relearn the whole skill: Interpret probability rule mistakes.
Sources and review
Original Mentora public practice, authored for this guide. Worked answers and syllabus mapping checked during editorial QA on 2026-09-11; no independent expert review is claimed. Graph connections are Mentora learning hints, not an official SEAB sequence. Read the source and examination-year notes.