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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)
11short 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?Show answer
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$. For mutually exclusive, $P(A \cap B) = 0$.
What is multiplication rule?Show answer
$P(A \cap B) = P(A) \cdot P(B | A)$. For independent, $P(B | A) = P(B)$ and $P(A \cap B) = P(A) P(B)$.
What is conditional probability?Show answer
$P(B | A) = P(A \cap B)/P(A)$.
What is multiplication principle?Show answer
$n$ ways for task $1$ and $m$ ways for task $2$ gives $nm$ ways combined.
What is permutations?Show answer
$^nP_r = \dfrac{n!}{(n-r)!}$.
What is combinations?Show answer
$^nC_r = \dfrac{n!}{r! (n-r)!}$.
What is with repetition?Show answer
$n^r$ ways to choose $r$ from $n$ with replacement.
What is using $^nP_r$ when order doesn't matter?Show answer
Selections are combinations.
What is forgetting that without replacement reduces population?Show answer
Second draw is from $n - 1$.
What is treating dependent events as independent?Show answer
Conditional probability is needed.
What is double counting in addition?Show answer
$P(A) + P(B)$ counts overlap twice.