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For two events A and B, suppose that P(A ∪ B) is at least 3/4 and the intersection probability satisfies 1/8 ≤ P(A ∩ B) ≤ 3/8. Statement-1: P(A) + P(B) is at least 7/8. Statement-2: P(A) + P(B) is at most 11/8. Choose the correct option: (a) Both statements are true, and Statement-2 correctly explains Statement-1. (b) Both statements are true, but Statement-2 does not correctly explain Statement-1. (c) Statement-1 is true and Statement-2 is false. (d) Statement-1 is false and Statement-2 is true.

1. Both statements are true, and Statement-2 correctly explains Statement-1.
2. Both statements are true, but Statement-2 does not correctly explain Statement-1.
3. Statement-1 is true and Statement-2 is false.
4. Statement-1 is false and Statement-2 is true.

Correct answer: Statement-1 is true and Statement-2 is false.

Solution

Statement-1 is true because the union of events A and B must account for their individual probabilities, leading to a minimum sum of 7/8 when considering the given intersection probabilities. Statement-2 is false because the maximum possible sum of their probabilities cannot exceed 1, making 11/8 an impossible scenario.

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