Kenneth ChengMathematical modeling
← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

Choose two distinct digits uniformly in order from 1,2,3,4,5 to form a two-digit number. Find the probability it is below 40.

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

Return to the lesson / paper ↗

TOPIC 01

2022 JM01

The digits cannot repeat, but the order matters.

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

Choose two distinct digits uniformly in order from 1,2,3,4,5 to form a two-digit number. Find the probability it is below 40.

Official paper · jm01-2022 · I.13 · PDF 3

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A1/51/5
  2. Option B2/52/5
  3. Option C3/53/5
  4. Option D4/54/5
  5. Option E11

Working and explanation

BUILD THE REASONING

Hint 1
The tens digit must be 1,2 or 3.
Hint 2
There are four choices for the units digit after each tens choice.
Worked solution

  1. Count all ordered pairs.

    N=5⋅4=20N=5\cdot4=20

  2. Count favourable pairs.

    Nf=3⋅4=12,P=12/20=3/5N_f=3\cdot4=12,\quad P=12/20=3/5

C: 3/5.

Checks and common pitfalls: The digits cannot repeat, but the order matters.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Count all ordered pairs.
    N=5⋅4=20N=5\cdot4=20
  • Count favourable pairs.
    Nf=3⋅4=12,P=12/20=3/5N_f=3\cdot4=12,\quad P=12/20=3/5

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 ↗