​If P(A) = 5/11, P(B) = 6/11 and P(A u B) = 8 /11 then​

Question

If \(P(A) = \frac 5{11}, P(B) = \frac 6{11}\) and \(P(A \cup B) = \frac 8{11}\) then \(P(A \cap B)\) =

(A) \(\frac 1{11}\)

(B) \(\frac 2{11}\)

(C) \(\frac 3 {11}\)

(D) \(\frac 9{11}\)

Answer 1

Correct option is (C) \(\frac 3{11}\)

P(A ∪ B) = \(\frac 8{11}\)

∴ P(A) + P(B) − P(A ∩ B) = \(\frac 8{11}\)

⇒ \(\frac 5{11} + \frac 6{11} - P(A\cap B)=\frac 8{11}\)

⇒ \(P(A\cap B) = \frac{11}{11} - \frac 8{11} = \frac 3{11}\)