Two fair dice, one red and one green, are rolled. Let the event \(A\) be the sum of the faces showing is equal to seven. Let the event \(B\) be the faces showing on the two dice are equal.

(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.

(f) How would you describe the relationship between event \(A\) and event \(B\) ?