P and Q are consider to apply for a job. The probability that P applies for the job is $\frac14$, the probability that applies for the job given that Q applies for the job is $\frac12$. and the probability that Q applies for the job given that P applies for the job is $\frac13$. Then the probability that P does not apply for the job given that Q does not apply for the job is

Let S be a sample space and two mutually exclusive events A and B be such that AUB=S.If P(^{.}) denotes the probability of the event, the maximum value of P(A)P(B) is ______.