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From a bag of t red and 2 blue balls, two are drawn without replacement. Given the first is red, find the probability the second is blue.

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

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

From a bag of t red and 2 blue balls, two are drawn without replacement. Given the first is red, find the probability the second is blue.

t=25t=25
  • 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
After a red draw, total=t+1 and blue=2.
Worked solution
  1. Express the event with a conditional probability or a disjoint partition.

  2. Apply the stated relation and retain its conditions.

    P=2/26P=2/26
  3. The color count and denominator must reflect the information already given.

The requested value is 0.0769230769231.

Checks and common pitfalls: The color count and denominator must reflect the information already given.

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 ↗