Separate disjoint prizes and subtract the entry fee once

A biased tetrahedral die is thrown onto a table; X is the number on the face in contact with the table. Its distribution is

x	$P(X=x)$
−1	$1/8$
0	$1/2$
2	$1/8$
3	$1/4$

(i) $X_1$ and $X_2$ are independent observations of X, and $Y=X_1+X_2$. Show that $P(Y=2)=3/16$.

(ii) A player pays 2 dollars to throw two such dice. The player receives 16 dollars if the maximum score is −1, or 3 dollars if the sum is prime, and receives nothing otherwise. Find the expected gain.