Let $(a, b, c, d)$ be integers where they are not necessarily different. If each one of them is in the set ($0$, $1$, $2$, $3$), what is the probability that $a \cdot d-b \cdot c$ is odd? (For example, ($0$, $3$, $1$, $1$) meet the condition, because $0 \cdot 1-3 \cdot 1=-3$ is odd.) 
选项为:A:$\frac3{16}$  B:$\frac14$  C:$\frac38$  D:$\frac12$  E:$\frac34$  请回答其中一个选项.