Kenneth ChengMathematical modeling
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Sampling with replacement chooses 2 people from a population of k+2. Find the probability the same person appears twice.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Statistics: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

Sampling with replacement chooses 2 people from a population of k+2. Find the probability the same person appears twice.

k=11k=11
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Identify the population and sampling mechanism before scaling counts.
Hint 2
Sum the mutually exclusive repeated-person outcomes.
Worked solution

  1. Identify the population and sampling mechanism before scaling counts.

  2. Calculate or simplify this relation.

    P=(13)(1/13)2=1/13P=(13)\left(1/13\right)^2=1/13

  3. This differs from sampling two distinct people without replacement.

The requested value is 0.07692308.

Checks and common pitfalls: This differs from sampling two distinct people without replacement.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗