A and B are disjoint with P(A)=P(B)=1/(k+2). Are they independent?
- 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
Compare the intersection probability with the product of probabilities.
Worked solution
Use independence only when justified and keep it distinct from disjointness.
Calculate or simplify this relation.
Positive-probability disjoint events are dependent.
No, their intersection probability is zero but the product of their probabilities is positive.
Checks and common pitfalls: Positive-probability disjoint events are dependent.
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.