FAD1015 Tutorial 1-6 — Counting & Probability Fundamentals
Tutorial questions covering Weeks 1-6 material: counting rules, permutations, probability fundamentals, conditional probability, independent events, Bayes' theorem, and random variables. Source file: FAD1015 Questions T1-T6 _20252026.pdf
Summary
Comprehensive problem set covering probability theory foundations from basic counting through discrete and continuous random variables.
Topics Covered
Tutorial 1: Counting Rules
- Multiplication principle
- Permutations of distinct objects
- Permutations with repetition
- Circular permutations
Tutorial 2: Advanced Counting
- Combinations
- Permutations of identical objects
- Mixed counting problems
Tutorial 3: Basic Probability
- Sample spaces and events
- Probability axioms
- Addition rule for mutually exclusive events
- Complement rule
Tutorial 4: Conditional Probability
- Definition and computation
- Multiplication rule
- Tree diagrams
- Law of total probability
Tutorial 5: Bayes' Theorem
- Prior and posterior probabilities
- Diagnostic testing problems
- Two-stage experiments
Tutorial 6: Random Variables
- Discrete random variables
- PDF and CDF
- Expected value and variance
- Continuous random variables (intro)
Key Formulas
Permutations:
- P(n,r) = n!/(n-r)!
- Circular: (n-1)!
- With repetition: nʳ
- Identical objects: n!/(n₁! × n₂! × ...)
Conditional Probability:
- P(A|B) = P(A∩B)/P(B)
- P(A∩B) = P(A|B) × P(B)
Bayes' Theorem:
- P(Bᵢ|A) = P(A|Bᵢ) × P(Bᵢ) / Σ P(A|Bⱼ) × P(Bⱼ)
Expected Value & Variance:
- E[X] = Σ x·P(X=x)
- Var(X) = E[X²] - (E[X])²
Related Lectures
- FAD1015 Week 1 — Counting Rules & Permutation
- FAD1015 Week 2 — Mutually Exclusive & Conditional Probability
- FAD1015 Week 3 — Independent Events & Bayes' Theorem
- FAD1015 Week 4 — Discrete Random Variables (PDF & CDF)
- FAD1015 Week 5 — Mean & Variance (Discrete & Continuous)
- FAD1015 Week 6 — Continuous Random Variables
Related Concepts
Related Course Page
- FAD1015 - Mathematics III