GATE CS 2017 Set 1 — Question 29

\(P\) and \(Q\) are considering to apply for a job. The probability that \(P\) applies for the job is \(\dfrac{1}{4}\), the probability that \(P\) applies for the job given that \(Q\) applies for the job is \(\dfrac{1}{2}\), and the probability that \(Q\) applies for the job given that \(P\) applies for the job is \(\dfrac{1}{3}\). Then the probability that \(P\) does not apply for the job given that \(Q\) does not apply for the job is