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HSC-EXT1 · Statistical Analysis

Statistical Analysis

HSC HSC Mathematics Extension 1 · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
ME-S1
Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

Teacher check

Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Statistical Analysis questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

2 marksext1-s1-1
Memoryless waiting time For the first-win waiting time XX, P(X>j)=(1−p)jP(X>j)=(1-p)^j with p=1/2p=1/2.
Part a · 2 marks

Show that P(X>1+4∣X>1)=P(X>4)P(X>1+4 | X>1)=P(X>4) and evaluate the common probability.

Worked solution

Answer: 1/16

  1. Conditional Probability: 1/16
  2. Index Laws: 1/16

Catalog reference: ext1_cssa25_geometric_memoryless_identity · seed 41001

Worked example 2

2 marksext1-s1-1
At least two matching dice 5 fair six-sided dice are rolled. Find the probability that at least two show a 3.
Part a · 2 marks

Give the exact probability.

Worked solution

Answer: 763/3888

  1. Binomial Complement: 3125/3888
  2. Probability: 763/3888

Catalog reference: ext1_cssa25_at_least_two_dice_successes · seed 41001

Worked example 3

3 marksext1-s1-1
Random vector sum Independently 4 times, choose with equal probability either 2i+3j2i+3j or 3i+2j3i+2j. Find the probability that the total is 10i+10j10i+10j.
Part a · 3 marks

Find the exact probability.

Worked solution

Answer: factorial(4) / ((factorial(2) factorial(2)) 16)

  1. Solve Vector Count: The target requires exactly 2 selections of each vector.
  2. Binomial Probability: binom(22,2)/2(22)binom(22,2)/2^(22).

Catalog reference: ext1_ind_2025_q13a_binomial_vector_sum · seed 41001

Content mapping and common errors

Statistical Analysis content identifiers

ME-S1

The Binomial Distribution

Apply the binomial distribution to probability problems; find mean and variance; use normal approximation.

Common student mistakes
  • ·Incorrect identification of p vs (1−p)
  • ·Applying the normal approximation without continuity correction

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

Other Extension 1 topics

Proof
1 content identifier
Vectors
1 content identifier
Trigonometric Functions
3 content identifiers
Functions
2 content identifiers
Calculus
3 content identifiers
Combinatorics
1 content identifier

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