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VICMath MethodsQuick questions

Unit 1: Functions, relations and graphs

Quick questions on Probability rules and combinations (VCE Maths Methods Unit 1)

10short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is complement?
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P(Ac)=1−P(A)P(A^c) = 1 - P(A).
What is addition rule?
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P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B). For mutually exclusive events, P(A∩B)=0P(A \cap B) = 0.
What is multiplication rule?
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P(A∩B)=P(A)⋅P(B∣A)P(A \cap B) = P(A) \cdot P(B|A). For independent events, P(B∣A)=P(B)P(B|A) = P(B), so P(A∩B)=P(A)P(B)P(A \cap B) = P(A) P(B).
What is conditional probability?
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P(B∣A)=P(A∩B)/P(A)P(B|A) = P(A \cap B)/P(A), the probability of BB given AA has occurred.
What is multiplication principle?
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If task 11 has n1n_1 ways and task 22 has n2n_2 ways, then the combined task has n1⋅n2n_1 \cdot n_2 ways.
What are permutations?
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Arrangements of rr items from nn:
What are combinations?
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Selections of rr from nn:
What is q1?
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How many ways can 55 books be arranged on a shelf? [1 mark]
What is q2?
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A committee of 33 is chosen from 55 teachers and 44 students. Find the probability it contains exactly 11 teacher. [3 marks]
What is q3?
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From 88 red and 22 white balls, 22 are drawn without replacement. Find P(at least one white)P(\text{at least one white}). [3 marks]

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