A total of $400$ new students at college were interviewed to find out if they either receive a scholarship, loan or no financial aid. There are $150$ male students, of which $50$ receive loan and $70$ do not receive any financial aid. One hundred female students receive scholarship. There are $140$ students who do not receive any financial aid. If a new student is selected at random, calculate the probability that the student is a

$($a$)$ female or a scholarship recipient.

$($b$)$ loan recipient if it is known that the student is female,

$($c$)$ male who is a scholarship recipient or female who receives a loan.

$($d$)$ female or non$-$scholarship recipient.