An event A has probability $\mathrm { P } ( \mathrm { A } ) = 0.3$.\ a) ( 0.75 points) An event B with probability $\mathrm { P } ( \mathrm { B } ) = 0.5$ is independent of A. Calculate $\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$.\ b) ( 0.75 points) Another event C satisfies $P ( C \mid A ) = 0.5$. Determine $P ( A \cap \bar { C } )$.\ c) (1 point) If there is an event D such that $P ( \bar { A } \mid D ) = 0.2$ and $P ( D \mid A ) = 0.5$, calculate $\mathrm { P } ( \mathrm { D } )$.
An event A has probability $\mathrm { P } ( \mathrm { A } ) = 0.3$.\
a) ( 0.75 points) An event B with probability $\mathrm { P } ( \mathrm { B } ) = 0.5$ is independent of A. Calculate $\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$.\
b) ( 0.75 points) Another event C satisfies $P ( C \mid A ) = 0.5$. Determine $P ( A \cap \bar { C } )$.\
c) (1 point) If there is an event D such that $P ( \bar { A } \mid D ) = 0.2$ and $P ( D \mid A ) = 0.5$, calculate $\mathrm { P } ( \mathrm { D } )$.