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QLDMath MethodsQuick questions

Unit 1: Algebra, statistics and functions

Quick questions on Probability rules and counting (QCE Math Methods Unit 1)

6short 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 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), subtracting the overlap so it is not counted twice. For mutually exclusive events P(A∩B)=0P(A \cap B) = 0, so the rule reduces to P(A)+P(B)P(A) + P(B).
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 \mid A), the chance of the first times the chance of the second given the first. For independent events P(B∣A)=P(B)P(B \mid 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 \mid A) = \dfrac{P(A \cap B)}{P(A)}, the probability of BB restricted to the world in which AA has happened. A tree diagram organises multi-stage experiments, with branch probabilities multiplied along a path and added across paths.
What is multiplication principle?
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nn ways for task 11 and mm ways for task 22 gives nmnm ways combined.
What are permutations?
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nPr=n!(n−r)!^nP_r = \dfrac{n!}{(n-r)!}.
What are combinations?
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nCr=n!r!(n−r)!^nC_r = \dfrac{n!}{r! (n-r)!}.

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