Consider two events $A$ and $B$ such that $P ( A ) = 0.5 , P ( B ) = 0.25$ and $P ( A \cap B ) = 0.125$. Answer in a reasoned manner or calculate what is requested in the following cases:\ a) (0.5 points) Let $C$ be another event, incompatible with $A$ and with $B$. Are events $C$ and $A \cup B$ compatible?\ b) (0.5 points) Are $A$ and $B$ independent?\ c) (0.75 points) Calculate the probability $P ( \bar { A } \cap \bar { B } )$ (where $\bar { A }$ denotes the event complementary to event A).\ d) (0.75 points) Calculate $P ( \bar { B } / A )$.