Independent Events (HSC SSCE Mathematics Advanced): Flashcards

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Independent Events
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Independent events definition

One event has no effect on probability of the other

Mathematical condition for independence using P(A∣B)P(A|B)

P(A∣B)=P(A)P(A|B) = P(A)

Alternative independence condition using P(B∣A)P(B|A)

P(B∣A)=P(B)P(B|A) = P(B)

Multiplication rule for independent events formula

P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B)

When can you use the multiplication rule

Only when events are independent

What multiplication rule tests and calculates

Both a test for independence and a calculation tool

Die (even) and coin (heads): P(A∩B)P(A \cap B)

14\frac{1}{4}

Best approach for 'at least one' probability problems

Use complement rule: 1−P(none)1 - P(\text{none})

Complement of 'at least one defective'

Neither defective

Are P(A∣B)=P(A)P(A|B) = P(A) and P(B∣A)=P(B)P(B|A) = P(B) equivalent

Yes, both are equivalent ways to express independence

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