Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 40% chance that she will fail the course if she does not have a tutor.
With a tutor, her probability of failing decreases to 10%. There is only a 50% chance that she will find a tutor at such short notice.
a. What is the probability that Christine fails the course?
b. Christine ends up failing the course. What is the probability that she had found a tutor?