A single fair die is rolled. Let the event \(A\) be the face showing is even. Let the event \(B\) be the face showing is divisible by 3 .

(a) List out the sample space of the experiment.

(b) List the outcomes in \(A\), and nd \(P(A)\).

(c) List the outcomes in \(B\), and nd \(P(B)\).

(d) List the outcomes in \(A \quad B\), and nd \(P\left(\begin{array}{ll}A & B\end{array}\right)\).

(e) Are the events \(A\) and \(B\) independent? Explain why or why not.