Use a weighted difference grid for two independent totals

An unbiased disc has one dot on one side and two dots on the other. The disc and an unbiased ordinary die are thrown; X is the sum of the disc dots and the dots on top of the die. Tabulate the distribution of X.

Show that $P(X\ge4\mid X\le7)=8/11$. Write down $E(X)$ and show that $\operatorname{Var}(X)=19/6$.

Two independent observations $X_1,X_2$ are taken.

(i) Find $\operatorname{Var}(X_1-X_2)$.

(ii) Find $P(X_1-X_2\ge5)$.