Kenneth ChengMathematical modeling
← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

For the same sample, find the expected number of defective items.

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

Return to the lesson / paper ↗

TOPIC 01

2024 JM01

An expected count need not be an integer.

Try it. Leave your reasoning visible.

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

01 / Standard#Your turn

For the same sample, find the expected number of defective items.

Official paper · jm01-2024 · II.1(b) · PDF 4

Official original and suggested answers ↗ · Suggested answer PDF page 6

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use an indicator for each of the four draws.
Hint 2
Each draw has marginal defective probability 3/10.
Worked solution

  1. Write the count as a sum.

    X=I1+I2+I3+I4,E(Ij)=3/10X=I_1+I_2+I_3+I_4,\quad E(I_j)=3/10

  2. Linearity does not require independence.

    E(X)=4(3/10)=6/5E(X)=4(3/10)=6/5

Expected count 6/5.

Checks and common pitfalls: An expected count need not be an integer.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Write the count as a sum.
    X=I1+I2+I3+I4,E(Ij)=3/10X=I_1+I_2+I_3+I_4,\quad E(I_j)=3/10
  • Linearity does not require independence.
    E(X)=4(3/10)=6/5E(X)=4(3/10)=6/5

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

Focus on one question

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

Curriculum and source notes ↗