Problem #2: (10pts) a) If the sets $X$ and $y$ are non-mutually exclusive, show that: $PCX cup Y)=P(X)+PCY)-PCX cap Y). b) Given two events $X$ and $y$, draw a Venn diagram to demonstrate that $PX)=P(X \cap Y)+PCX \cap barty))$, and deduce that $PX)=P(X/Y) PCY+PCX / Xbar(Y)) P(\bar Y})$. SP.S0.01