Two dice are rolled. The red die has been loaded. Its probabilities are \(P(1)=P(2)=P(3)=P(4)=\frac{1}{5}\) and \(P(5)=P(6)=\frac{1}{10}\). The green die is fair. Let the event \(A\) be the sum of the faces showing is an even number. Let the event \(B\) be the sum of the faces showing is divisible by 3 .

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

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

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

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