A student feels that 70% of her college courses have been enjoyable and the remainder have been boring. This student has access to student evaluations of professors and finds out that professors who had previously received strong positive evaluations from their students have taught 60% of his enjoyable courses and 25% of his boring courses. Next semester the student decides to take three courses, all from professors who have received strongly positive student evaluations. Assume that this student's reactions to the three courses are independent of one another.
a. What is the probability that this student will find all three courses enjoyable?
b. What is the probability that this student will find at least one of the courses enjoyable?