Kenneth ChengMathematical modeling
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Find P(A|B) from the given probabilities.

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

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TOPIC 01

Random variables and distributions: mixed review

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 / Foundation#Your turn

Find P(A|B) from the given probabilities.

P(A∩B)=1/24,P(B)=2/24P(A\cap B)=1/24,\quad P(B)=2/24
  • The conditioning event must have positive probability; a total-probability partition is exhaustive and disjoint.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Express the event with a conditional probability or a disjoint partition.
Hint 2
Use this intermediate relation.
P(A∣B)=P(A∩B)/P(B)P(A|B)=P(A\cap B)/P(B)
Worked solution

  1. Express the event with a conditional probability or a disjoint partition.

  2. Apply the stated relation and retain its conditions.

    P(A∣B)=(1/u)/(2/u)=1/2P(A|B)=(1/u)/(2/u)=1/2

  3. Restrict the sample space to B.

The requested value is 0.5.

Checks and common pitfalls: Restrict the sample space to B.

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 ↗