semester EN couse, one third of sud siology course succestols, they will ta$,8$ hous a day with probably, and iven that they fail the Brology course, they will study $8$ hours a day with probablity $,.$ Ifa student passes the Biology couse successfully and studios $8$ hours a day, he registers for the Micro$-$biology course with probablity $.$ On the other hand, the probability of registering for the Micro. biology course is reduced to H if he does not pass the Biology course and he does not study for $8$ hours. In other situations passing the Biology course and not studying for $8$ hours a day, fail the Biology course and study for $8$ hours the probability of registering for the Micro$-$biology course is $0\mathrm{.}25.$a$)$ What is the probability that the student does not pass the Biology course and he studies $8$ hours a day and he does not register for the Micro$-$biology course?b$)$ What is the probability that he registers for the Micro$-$biology course?c$)$ Given that he registers for the Micro$-$biology course, what is the probability that he passed the Biology course? $(10$ marks$)$