Let \(S\) be a sample space and two mutually exclusive events \(A\) and \(B\)…

Let \(S\) be a sample space and two mutually exclusive events \(A\) and \(B\) be such that \(A \cup B = S\). If \(P(.)\) denotes the probability of the event, the maximum value of \(P(A)P(B)\) is_____.