The probability of each component failing is 1/(k+1), but common power failures can affect both. Can the independent-series formula be used without further evidence?
- Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Use independence only when justified and keep it distinct from disjointness.
Hint 2
Inspect shared causes, not just marginal probabilities.
Worked solution
Use independence only when justified and keep it distinct from disjointness.
Calculate or simplify this relation.
A numerical marginal rate does not establish independence.
No; a shared cause may create dependence.
Checks and common pitfalls: A numerical marginal rate does not establish independence.
Reasoning checklist · self / teacher assessment
- State the relevant definition, condition or model.
- Show a valid calculation, proof or counterexample.
- Interpret the conclusion with its restrictions.
Think first. Reveal a hint when the class is ready.