“Given that B”?
Restrict attention to B.
H1 MATHEMATICS · CONDITIONAL PROBABILITY
Change the sample space.
Then calculate.
A focused guide for Singapore A-Level H1 Mathematics syllabus 8865. Turn “given that” into the correct denominator, then check whether the events are truly independent.
- Correct “given that” reasoning
- Independence checks
- Exam-language reminders
Built around 8865 H1 MathematicsProbability rules, conditional probability and independence
Useful during examination revisionRecognise the words before pressing the calculator
THE CENTRAL DISTINCTION
Restricted is not independent
P(A | B) asks for the proportion of B that also lies in A. The information that B occurred changes the sample space.
Independence is a separate claim: knowing B does not change the probability of A, so P(A | B) = P(A).
THREE CHECKS
Read the relationship before using a rule
Independent?
Check a valid equivalent condition; do not assume it from the wording.
Mutually exclusive?
The events cannot happen together.
WORKED EXAMPLE
Use the denominator named by the condition.
In a class, 60% revise with notes N, 45% attempt timed papers T, and 30% do both. Find P(N | T) and determine whether N and T are independent.
EXAM HABIT
Write the conditional-probability fraction before substituting values.
- 1
Identify the restricted group
The condition is T, so P(T) is the denominator.
- 2
Calculate the conditional probability
- 3
Test independence
Therefore N and T are not independent.
AnswerP(N | T) = 2/3; the events are not independent.
COMMON MISTAKES
What to catch before the examiner does
Reversing the condition
P(A | B) and P(B | A) usually have different denominators and different values.
Equating “disjoint” with “independent”
Non-empty mutually exclusive events are not independent: one occurring rules out the other.
Assuming independence
Verify it using probabilities unless the question explicitly states it.
Losing the context
State conclusions about the actual events, not only symbols or calculator output.
PRACTISE WITH FEEDBACK
Show the probability model, not only the answer.
Submit typed or handwritten working and ask Integrand to check the event definitions, denominator and conclusion.
Try Integrand- 1
Define
Name each event clearly.
- 2
Represent
Use a table, tree or Venn diagram.
- 3
Conclude
Answer in the language of the question.
QUICK QUESTIONS
H1 conditional probability FAQ
What does “given that” mean in probability?
It restricts the sample space to the event after the vertical bar. That event supplies the denominator in the conditional-probability formula.
How do I test whether two events are independent?
Check whether P(A ∩ B) = P(A)P(B), or equivalently whether P(A | B) = P(A) when P(B) is non-zero.
Is this guide within the H1 syllabus?
Yes. Conditional probabilities in simple cases, probability rules and independence are included in Singapore A-Level H1 Mathematics syllabus 8865.
READY TO PRACTISE?