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

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

P(A) + P(B) ≤ 11/8

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

None of these

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P(A∩B) = P(A) + P(B) − P(A∩B)

∴ 1 ≥ P(A) + P(B) − P(A∩B) ≥ 3/4.
But minimum of P(A∩B) =18

$∴ P (A) + P (B) - \frac{1}{8} \geq 3 / 4$

$\Rightarrow P (A) + P (B) \geq \frac{7}{8}$
As the maximum of $P (A \cap B) = \frac{3}{8}$

∴ 1 ≥ 1P(A) + P(B) − 3 / 8

⇒ P(A) + P(B) ≤ 11 / 8

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