A college student is planning to apply for a school grant. A friend of hers who works for the company that is offering the grant has told her that if she takes calculus in her freshman year and gets as A or B, she will be very strongly considered for the grant, but if she gets a C, D or F, she will probably not be considered. If she doesn't take calculus at all, she will remain a candidates She estimates the following probabilities:
Probabilities of getting the grant if she takes calculus and gets A or B: 0.80
Probabilities of getting the grant if she takes calculus and gets C, D or F: 0.10
Probabilities of getting the grant if calculus not taken: 0.50
Probabilities of getting A or B in calculus: 0.60
What is the probability that she will get the grant if she takes calculus? What should she do to maximize the probability that she will get the grant?