There is a canteen in a university and students from engineering department and architecture de$-$

partment use it$.$ Inter$-$arrival time of male engineering students, female engineering students, male

architecture students and female architecture students are exponentially distributed random vari$-$

ables. The average inter$-$arrival time of male engineering students is $30$ minutes, female engineering

students is $20$ minutes, male architecture students is $15$ minutes and female architecture students

is $60$ minutes. If only $2$ students have arrived before $10AM$ in the morning, what is the probability

that the first student arriving after $10AM$ is a architecture student if we know that the student is

not a male engineering student?

$($a$)\frac{1}{2}$

$($b$)\frac{2}{3}$

$($c$)\frac{2}{5}$

$($d$)\frac{5}{8}$

$($e$)1$