Part BCSIR NET June 2024conditioning-is-a-measure-only-for-fixed-condition

Conditioning is a measure only for fixed condition

Let $A_{1}, A_{2}, A_{3}$ be events satisfying $0 < P(A_{i}) < 1$ for i = 1, 2, 3. Which of the following statements is true?

A. $P(A_{1}$ | $A_{2})P(A_{2}$ | $A_{3}) \le P(A_{1}$ | $A_{3})$
B. $P(A_{1}$ | $A_{2})P(A_{3}$ | $A_{2}) \ge P(A_{1} \cap A_{3}$ | $A_{2})$
C. $P(A_{1}$ | $A_{2}) + P(A_{3}$ | $A_{2}) \ge P(A_{1} \cup A_{3}$ | $A_{2})$ ✓ Correct
D. $P(A_{1}$ | $A_{2}) + P(A_{2}$ | $A_{3}) \le P(A_{1}$ | $A_{3})$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests dependence misread.

See pricing

50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

Related counterexample: Pairwise independent events are mutually independent

Conditioning is a measure only for fixed condition

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