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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.
- Both statements are true, and Statement-2 correctly explains Statement-1.
- Both statements are true, but Statement-2 does not correctly explain Statement-1.
- Statement-1 is true and Statement-2 is false.
- Statement-1 is false and Statement-2 is true.
Correct answer: Both statements are true, but Statement-2 does not correctly explain Statement-1.
Solution
Since P(A)+P(B)=P(AuB)+P(A∩B): minimum = 3/4 + 1/8 = 7/8 (Statement 1 true), maximum = 1 + 3/8 = 11/8 (Statement 2 true). Both are true but they use different bounds, so Statement 2 does not explain Statement 1 -> option (b).
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