WBJEE · Maths · Probability
If \(A, B\) 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
- A \(P(A)+P(B) \leq \frac{11}{8}\)
- B \(P(A) \cdot P(B) \leq \frac{3}{8}\)
- C \(P(A)+P(B) \geq \frac{7}{8}\)
- D None of the above
Answer & Solution
Correct Answer
(C) \(P(A)+P(B) \geq \frac{7}{8}\)
Step-by-step Solution
Detailed explanation
We know, \[ P(A \cup B)=P(A)+P(B)-P(A \cap B) \] \(\Rightarrow P(A)+P(B)=P(A \cup B)+P(A \cap B)\) Given, \(\quad \frac{3}{4} \leq P(A \cup B) \leq 1\) and \(\quad \frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8}\) So.…
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