Let A and B be two events such that P(AUB) ≤ 3/4 and 1/8 ≤ P(A⋂B) ≤ 3/8.Statement 1: P(A) + P(B) ≥ 7/8statement 2: P(A) + P(B) ≤ 11/8

Engineering

Mathematics

Conditional Probability

Question

Let A and B be two events such that P(AUB) ≤ 3/4and 1/8 ≤ P(A⋂B) ≤ 3/8.
Statement 1: P(A) + P(B) ≥ 7/8
statement 2: P(A) + P(B) ≤ 11/8

Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

Both the statements are TRUE and STATEMENT 2 is not the correct explanation of STATEMENT 1.

STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.

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$P(AUB) = P(A) + P(B) - (A⋂B)$

$\frac{3}{4} \leq P (A \cup B) \leq 1$

$\frac{3}{4} \leq P (A) + P (B) - P (A \cap B) \leq 1$

$\frac{3}{4} + P (A \cap B) \leq P (A) + P (B) \leq 1 + P (A \cap B)$

$\frac{3}{4} + \frac{1}{8} \leq P (A) + P (B) \leq 1 + \frac{3}{8}$

$\frac{7}{8} \leq P (A) + P (B) \leq \frac{11}{8}$
both the statements are correct but statement 1 is not the correct explanation of statement 2

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