Two indicator variables that are neither identically distributed nor independent

Suppose that $\Omega_1=\{1,2,3,4,5,6\}$ and that P is a probability measure such that $P(\{j\})=1/6$ for $j=1,\dots,6$. Let $I_A$ and $I_B$ be the indicator functions of the subsets $A=\{1,3,5\}$ and $B=\{2,3,4,6\}$ respectively. Consider: (I) $I_A$ and $I_B$ are identically distributed. (II) $I_A$ and $I_B$ are independent random variables.