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Let A and E be any two events with positive probabilities Statement I: P(E/A) ≥ P(A/E)P(E). Statement II: P(A/E) ≥ P(A ∩ E). (1) Both the statements are false (2) Both the statements are true (3) Statement - I is false, Statement - II is true (4) Statement - I is true, Statement - II is false

1. Both the statements are false
2. Both the statements are true
3. Statement - I is false, Statement - II is true
4. Statement - I is true, Statement - II is false

Correct answer: Both the statements are true

Solution

Both statements are true because they correctly reflect the relationships defined by conditional probabilities and the properties of probability measures. Statement I follows from the definition of conditional probability, while Statement II is a consequence of the fact that the probability of an event given another cannot exceed the probability of the event itself.

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