Last updated on Oct 23, 2026

Conditional Probability Formulae (HSC SSCE Mathematics Advanced): Quizzes

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Conditional Probability Formulae

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What does $P(A|B)$ represent?

Probability of A given B has occurred

What happens to the sample space when event $B$ occurs in conditional probability?

It reduces to just outcomes within B

Which formula applies when outcomes are equally likely?

$P(A|B) = \frac{|A \cap B|}{|B|}$

What does $|A \cap B|$ represent in the cardinality formula?

Number of outcomes in both A and B

When should you use $P(A|B) = \frac{P(A \cap B)}{P(B)}$ rather than the cardinality formula?

When you have probabilities not counts

In a survey, 50 like science and 30 like both subjects. What is $P(\text{math}|\text{science})$ ?

$\frac{3}{5}$

In quality control: 10% defective, 90% detection, 5% false positive. What is $P(\text{positive})$ ?

$0.135$

Which method is ideal for sequential events when calculating joint probabilities?

Tree diagrams

In tree diagrams, what must all probabilities at each branch point sum to?

$1$

What condition must be met for $P(A|B)$ to be defined?

$P(B) \neq 0$

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Conditional Probability Formulae (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What does P(A∣B)P(A|B)P(A∣B) represent?

What happens to the sample space when event BBB occurs in conditional probability?

Which formula applies when outcomes are equally likely?

What does ∣A∩B∣|A \cap B|∣A∩B∣ represent in the cardinality formula?

When should you use P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}P(A∣B)=P(B)P(A∩B)​ rather than the cardinality formula?

In a survey, 50 like science and 30 like both subjects. What is P(math∣science)P(\text{math}|\text{science})P(math∣science)?

In quality control: 10% defective, 90% detection, 5% false positive. What is P(positive)P(\text{positive})P(positive)?

Which method is ideal for sequential events when calculating joint probabilities?

In tree diagrams, what must all probabilities at each branch point sum to?

What condition must be met for P(A∣B)P(A|B)P(A∣B) to be defined?

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

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Solve Equations

Introduction to Functions and Relations

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Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

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Introduction to Rates of Change

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Exponential Functions

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Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

What does $P(A|B)$ represent?

What happens to the sample space when event $B$ occurs in conditional probability?

What does $|A \cap B|$ represent in the cardinality formula?

When should you use $P(A|B) = \frac{P(A \cap B)}{P(B)}$ rather than the cardinality formula?

In a survey, 50 like science and 30 like both subjects. What is $P(\text{math}|\text{science})$ ?

In quality control: 10% defective, 90% detection, 5% false positive. What is $P(\text{positive})$ ?

What condition must be met for $P(A|B)$ to be defined?