Question
Download Solution PDFIf two events A and B such that P(A ∪ B) = \(\frac{7}{8}\) and P(A ∩ B) = \(\frac{1}{4}\) and P(A) = \(\frac{5}{8}\), then P\((\overline{A} ∪ \overline{B})\) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given, P(A ∪ B) = \(\frac{7}{8}\) and P(A ∩ B) = \(\frac{1}{4}\) and P(A) = \(\frac{5}{8}\)
To find: P\((\overline{A} ∪ \overline{B})\) = ?
Since, \(P(A\cap B)+P(\overline{A\cap B})=1\)
⇒ \(P(\overline{A\cap B})=1-P(A\cap B)\)
⇒ \(P(\overline{A\cap B})=1-\frac{1}{4}\)
⇒ \(P(\overline{A\cap B})=\frac{3}{4}\)
We know that, \(P(\overline{A}\cup \overline{B})=P(\overline{A\cap B})\)
Hence, \( P(\overline{A}\cup \overline{B})=\frac{3}{4}\)
Last updated on May 26, 2025
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