engineering recuitment GATE CSE 2023-24 Test Series Engineering Mathematics Probability Conditional Probability
P and Q are considering to apply for a job. The probability that P applies for the job is \(\frac{1}{4}\), the probability that P applies for the job given that Q applies for the job is \(\frac{1}{2}\), and the probability that Q applies for the job given that P applies for the job is \(\frac{1}{3}\). The probability that P does not apply for the job given that Q does not apply for the job is \(P\left( {\frac{{P'}}{{Q'}}} \right)\)and the probability that P apply for the job or Q apply for the job is \(P\left( P \cup Q \right)\). Which of the following is/are TRUE?
1
\(P\left( {\frac{{P'}}{{Q'}}} \right) = \frac{4}{5}\)
2
\(P\left( P \cup Q \right) = \frac{1}{4}\)
3
\(P\left( P \cup Q \right) = \frac{1}{3}\)
4
\(P\left( {\frac{{P'}}{{Q'}}} \right) = \frac{3}{5}\)