If 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\((\overline{A} ∪ \overline{B})\) = ?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 2 Official Paper

Answer 1

Explanation:

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, \( P(\overline{A}\cup \overline{B})=\frac{3}{4}\)