We define three random variables in $\{0,1\}(0=$ false, $1=$ true$)$:

$$ person X likes coding $($LC$),$

$$ person X is hard$-$working $($HW$),$ and

$$ person X attends GSU $($GSU$).(15$ points$)$ We define three random variables in false, $1=$ true$)$:

person X likes coding $($LC$),$

person $x$ is hard$-$working $($HW$),$ and

person X attends GSU $($GSU$).$

The probabilities are given below:

a$.$ Is "Person $x$ likes coding" independent of "person $x$ is hard$-$working"? Why or why not?

b$.$ Is "person X likes coding" conditionally independent of "person $x$ is hardworking" given "person $x$ attends

GSU"? Why or why not?

c$.$ If person is attends to GSU, what is the probability of person is hardworking?