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Independent Events (HSC SSCE Mathematics Advanced): Quizzes

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Independent Events

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What defines two events as independent?

One event's outcome doesn't affect the other

Which equation shows events $A$ and $B$ are independent?

$P(A|B) = P(A)$

What is the multiplication rule for independent events $A$ and $B$ ?

$P(A \cap B) = P(A) \times P(B)$

When can you use $P(A \cap B) = P(A) \times P(B)$ ?

Only when events are independent

Are rolling a die and flipping a coin independent events?

Yes, the die outcome doesn't affect coin

If $P(A) = 0.3$ and $P(B) = 0.4$ (independent), find $P(A \cap B)$ .

$0.12$

To test independence, check if $P(A \cap B)$ equals what?

$P(A) \times P(B)$

For 'at least one' problems with independent events, which approach is most efficient?

Find $P$ (none), then subtract from $1$

Are conditions $P(A|B) = P(A)$ and $P(B|A) = P(B)$ equivalent for independence?

Yes, both express independence equally

If $P$ (defect) $= 0.02$ per item (independent), find $P$ (at least one defect in two items).

$0.0396$

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Independent Events (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What defines two events as independent?

Which equation shows events AAA and BBB are independent?

What is the multiplication rule for independent events AAA and BBB?

When can you use P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B)P(A∩B)=P(A)×P(B)?

Are rolling a die and flipping a coin independent events?

If P(A)=0.3P(A) = 0.3P(A)=0.3 and P(B)=0.4P(B) = 0.4P(B)=0.4 (independent), find P(A∩B)P(A \cap B)P(A∩B).

To test independence, check if P(A∩B)P(A \cap B)P(A∩B) equals what?

For 'at least one' problems with independent events, which approach is most efficient?

Are conditions P(A∣B)=P(A)P(A|B) = P(A)P(A∣B)=P(A) and P(B∣A)=P(B)P(B|A) = P(B)P(B∣A)=P(B) equivalent for independence?

If PPP(defect) =0.02= 0.02=0.02 per item (independent), find PPP(at least one defect in two items).

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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

Which equation shows events $A$ and $B$ are independent?

What is the multiplication rule for independent events $A$ and $B$ ?

When can you use $P(A \cap B) = P(A) \times P(B)$ ?

If $P(A) = 0.3$ and $P(B) = 0.4$ (independent), find $P(A \cap B)$ .

To test independence, check if $P(A \cap B)$ equals what?

Are conditions $P(A|B) = P(A)$ and $P(B|A) = P(B)$ equivalent for independence?

If $P$ (defect) $= 0.02$ per item (independent), find $P$ (at least one defect in two items).