If A and B are two events such that and , then

Engineering

Mathematics

Conditional Probability

Question

If A and B are two events such that $P (A \cup B) \geq \frac{3}{4}$ and $\frac{1}{8} \leq P (A \cap B) \leq \frac{3}{8}$ , then

$P (A) + P (B) \leq \frac{11}{8}$

$P (A) \cdot P (B) \leq \frac{3}{8}$

$P (A) + P (B) \geq \frac{7}{8}$

None of these

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P(A⋃B) = P(A) + P(B) − P(A∩B)

$∴ 1 \geq P (A) + P (B) - P (A \cap B) \geq \frac{3}{4}$
As the minimum value of $P (A \cap B) = \frac{1}{8}$
we get $P (A) + P (B) - \frac{1}{8} \geq \frac{3}{4} \Rightarrow P (A) + P (B) \leq 1 + \frac{3}{8} = \frac{11}{8}$

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