A biology professor gives two exams and a final in the course. The professor has noticed that80% of students get a B or better on exam 1.If a student gets a B or better on exam 1 then chance of passing the final exam is 73%.If a student gets lower than a B on exam 1 then there is a 45% chance of passing the final exam.

a) Suppose a student passes the final exam.What is the probability that the student got C or lower on the first exam?Write the question using function notation.

b) What is the probability that a student passes the final exam?Write the question using function notation

c) Suppose the professor in question 1 polls five students to see if they liked the Biology book that was used for the course.Let the random variable X measure the number of students that say they liked the book.Write out the sample space for the variable X.