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Disjoint events have probabilities 1/(k+3) and 2/(k+3). Find their union probability.

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

TOPIC 01

Probability: 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 / Foundation#Your turn

Disjoint events have probabilities 1/(k+3) and 2/(k+3). Find their union probability.

k=8k=8
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Describe the sample space and event sets, then count or apply a probability identity.
Hint 2
Disjointness removes the overlap term.
Worked solution
  1. Describe the sample space and event sets, then count or apply a probability identity.

  2. Calculate or simplify this relation.

    P(A∪B)=1/11+2/11=3/11P(A\cup B)=1/11+2/11=3/11
  3. Mutually exclusive does not mean independent.

The requested value is 0.27272727.

Checks and common pitfalls: Mutually exclusive does not mean independent.

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 ↗