Year 11 Maths Advanced MAV-11-09 Checkpoint 1

Checkpoint Quiz 1

This checkpoint covers Probability Rules, Conditional Probability, Independence and Mutual Exclusivity, and Discrete Probability Distributions (Lessons 1–5).

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Quick Review

  • Addition rule: $P(A \cup B) = P(A)+P(B)-P(A \cap B)$. Simplifies to $P(A)+P(B)$ only when $A$ and $B$ are mutually exclusive, that is, $P(A \cap B) = 0$.
  • Multiplication rule: $P(A \cap B) = P(A) \times P(B \mid A)$. Simplifies to $P(A) \times P(B)$ only when $A$ and $B$ are independent, do not assume it, check it.
  • Conditional probability: $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$. In a two-way table, condition on the column or row total, never the grand total.
  • Independence vs mutual exclusivity: Independent means $P(A \cap B) = P(A) \times P(B)$, the Venn circles can still overlap. Mutually exclusive means $P(A \cap B) = 0$, and if both probabilities are positive, mutually exclusive events are always dependent.
  • Discrete probability distributions: A valid distribution needs $0 \leq P(X=x) \leq 1$ and $\sum P(X=x) = 1$. The expected value $E(X) = \sum x \cdot P(X=x)$ is the long-run average, it does not need to be an achievable value of $X$.
MC

Multiple Choice

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